Nobel lecture of Harvey Alter

In 2020 the Nobel prize for medicine was awarded to Harvey Alter, Michael Houghton and Charles Rice for their role in the discovery of the hepatitis C virus. I now watched the videos of the corresponding Nobel lectures. For my taste the lecture of Alter was by far the most interesting of the three. I think that he was also the one who played the most fundamental role in this discovery. At the beginning of his lecture he emphasizes the point that the most important discoveries in science often come as a complete surprise and not as a result of planned research programmes. Alter was 85 when he got the prize and so he had to wait a long time for it. The papers documenting his fundamental contributions were published in 1989. A central part of this work was the collection and preservation of blood samples from patients undergoing open heart surgery. Why was this group chosen? One of the most important modes of infection with hepatitis B and C used to be blood transfusions. This continued to be the case until tests were available to screen donors for these diseases. This kind of surgery involves extensive blood transfusions and so the chances of infection were relatively high in these patients. Also these patients suffered from relatively few other diseases which could have been confounding factors. These blood samples were an invaluable resource in the search for the virus. They were the basis of painstaking analysis over many years.

One important feature of hepatitis C is that it becomes chronic in 70 per cent of cases. This looks like a failure of the immune system to handle this disease. What are the reasons for this failure? One concerns quasispecies. The hepatitis C virus has an RNA genome and the copying of RNA is very error-prone. This leads to a huge variety in the genomes of virions in a single patient. This in turn results in rapid mutations of the virus. If an antibody has developed to combat the virus then selective pressure will quickly cause a new form to become dominant which is not vulnerable to that antibody. It seems to me that if this type of effect is to be captured using mathematical model it will require a stochastic model. Deterministic models of the type I have studied in the past are probably not helpful for that. In the lecture it is also mentioned that the number of T cells (CD4+ and CD8+) declines very much in chronically infected hepatitis C patients. No explanation is offerred as to why that is the case. Deterministic mathematical models might be able to contribute some understanding in that case.

The lecture contains the following interesting story. There was a time at which liver cancer was much more common in Japan than in the West. The reason for this was that that cancer was in many cases a late stage effect of hepatitis C. During wars in the early part of the 20th century many Japanese soldiers injected drugs with shared needles and this was what spread the disease. It was observed that there were many cases of jaundice (the most striking symptom of hepatitis) on the battlefield. Decades later many of these men developed serious liver disease, including cancer. Japanese doctors predicted that a similar phenomenon would be seen in the West when the effects of recreational drug use became manifest. They were right.

Fighting homeopathy

Most health systems in the world have financial problems and Germany is no exception to this. As a scientifically educated person it seems to me outrageous that the public health system here in Germany should spend money on homeopathic treatments. There is hardly anything in the area of ‘alternative medicine’ which is based on ideas which so blatantly contradict scientific reasoning. I was thus very glad to see that the health minister Karl Lauterbach has announced that he wants to ban the public health system from paying for homeopathic treatments. It is not the first time that a politician has tried this and suggestions of this type are usually greeted by a storm of opposition. I am not very optimistic that the idea of stopping public funds being used to finance homeopathy will actually find a sufficiently strong political consensus so as to result in legislation. If the idea actually succeeded I would be very happy. Of course the loudest opposition comes from those who earn money with homeopathy. One argument used is that the money involved is a small part of the total costs of the public health system. Of course it is the duty of those responsible to make sure that government money spent on health is well spent. The standards are usually very high. Often people cannot get treatments paid which are probably valuable but where the level of evidence required has not been reached. Thus I see the issue of homeopathy is one of principle. It is an insult to someone who is seriously ill and has to accept that the health insurance cannot pay for a treatment which would probably be effective (but is not yet provably so) while it pays for quackery. Germany has made a lot of important contributions to medicine but it should not be forgotten that although the disease homeopathy (as I see it) is widespread in the world it had its origin in Germany.

Karl Lauterbach is quite open about the fact that it is not the amount of money which is the central point. He is a scientist and qualified as a medical doctor and acts according to the ethical principles of these disciplines. He became publicly known through his role in the COVID-19 pandemic. (His academic speciality is epidemiology and public health.) During the pandemic he tended towards recommending strict measures and in this way he made himself unpopular with many people. At the same time his role was appreciated by many others (including myself) and this led to his appointment as health minister. He is a member of the SPD, having switched a long time ago from the CDU. Some politicians of other parties have accused him of using the issue of homeopathy to direct people’s attention away from other parts of his health policy which are seen as unsuccessful. I feel sure that this is not true. It is typical of Lauterbach, during the pandemic and otherwise, that he publicly says what he believes to be the truth, even when that results in unpopularity and attacks on him in the media. Although there are many aspects of Lauterbach’s politics I do not agree with I tend to identify with him as a person. I see him as a representative of honesty and rationalism in the public domain. The fact that many of the attacks on him involve personal antipathy and making fun of his appearance only tend to strengthen my feeling of solidarity with him.

It might be said that politicians have more important things which they should concentrate on than homeopathy but I am not prepared to accept that. I think that in the long term the struggle between science and superstition is a matter of key importance for the future of our civilization.

Nobel lectures of Katalin Karikó and Drew Weissman

Yesterday I listened to the Nobel lectures of Katalin Karikó and Drew Weissman, describing their work on mRNA vaccines. The lecture of Karikó mainly described the history of their discoveries while that of Weissman went into more technical details and discussed the prospects for the future applications of this technology. One interesting aspect of Karikó’s lecture was what she said about the difficulties she experienced during her scientific career. She was repeatedly unable to obtain funding for her research and lost several jobs due to her lack of success in this endeavour. For many years her work was supported by sympathetic colleagues. She could not afford assistants and had to do the menial jobs in the lab herself, down to thawing out the fridge where she kept her samples. In her talk she did not complain loudly about the injustice done to her in this way but restricted herself to making brief comments along the way. Eventually her career was saved when she was given a good job at the then obscure company Biontech.

Now let me come to the science, following Karikó’s account. After mRNA was discovered it took about twenty years before it could be synthesized artificially. mRNA is the template for the production of proteins and this gives rise to the idea that it might be made to cause cells to produce desirable proteins, for instance drugs. It turned out that there are several problems with this. The first is that within a living organism mRNA is attacked by the immune system and destroyed. The second is that artifical mRNA seemed to give poor protein yields. The third is that mRNA is a rather unstable molecule and thus only survives for a short time after it has been introduced into the body. Artificial mRNA is like the molecule is described in the textbooks. It consists of a string of nucleotides each of which contains one of the bases adenine, cytosine, guanine and uracil. Natural mRNA as it occurs in the human body is very different since many of the nucleotides containing the bases have been chemically modified. At the beginning of the work described in the lecture the enzymes responsible for these modifications were not known so that this process could not be understood, let alone controlled. A key type of experiment done by Karikó and Weissman was to feed dendritic cells with nucleotides, natural or modified, and look at whether they showed an inflammatory reaction, producing cytokines. It turned out that the dendritic cells reacted much less strongly to mRNA including certain modified nucleotides occuring naturally than to the textbook mRNA. It is easy to guess why this should be the case. (This is my speculation, not a statement from the lecture.) mRNA occurring in the body could be from a pathogen such as a virus and then the immune system should eliminate it. The modifications could be a way the body could signal to the immune system that an mRNA molecule is made by the host and should be left alone. In any case it was found by trying many examples that one powerful way of suppressing the immunogenicity of the RNA was to replace uridine by the modified molecule pseudouridine. This provided an avenue to removing the first of the difficulties in applying RNA therapeutically. It turns out that the modified RNA produces higher protein yields and is more stable than the textbook RNA. In other words, it can contribute to the solution of the other two problems as well.

If RNA is to be used as a vaccine then while the immune system should ignore the RNA it should react strongly to the corresponding protein. This seemed to work well in the case of RNA vaccines but this was paradoxical. Normally a protein is not enough to make a vaccine. It must be accompanied by another substance, an adjuvant, which activates the innate immune system. The RNA vaccine contained no known adjuvant. The solution to this problem is as follows. In order to get the RNA into a cell it has to be coated in lipids. It turns out that these lipids act as an adjuvant. In the end they activate the so-called follicular helper T cells. This kind of vaccine is remarkable in that it can stimulate the immune system more strongly than the pathogen it is intended to be a vaccine against. For instance the RNA vaccines against COVID-19 cause a production of antibodies which is several times higher than an infection with the virus itself.

Now a lot is known about the use of different kinds of RNA to achieve different effects. Various aspects of this were explained in the lecture of Weissman. He discussed a variety of different applications which appear within reach: improved vaccines against infectious diseases, vaccines against cancer, production of drugs. Appart from their flexibility and effectiveness the RNA techniques have the potential to replace the extremely expensive processes required for the therapy of certain diseases by rather cheap ones. Weismann’s talk gave the impression that the RNA techniques could soon lead to revolutionary advances in medicine. He is not at all the type of person who comes across as an advertiser. Instead he makes an impression of someone who is modest and trustworthy. He discussed a wide variety of examples. Let me concentrate on one. This is the idea of a universal influenza vaccine. The influenza virus mutates frequently with the result that it is necessary to develop a new vaccine each year to be effective for the new dominant variant. A dream is to develop a vaccine which would be effective for all types. It has been found that RNA vaccines can be effective against many antigens simultaneously, for instance for all types of influenza. This is being tested in practice now. I was excited by what I heard in this lecture. Of course there will no doubt be many unexpected difficulties in implementing these ideas but I think that there is a good chance that they could bring a major improvement in medicine as a whole.

Talk on personalized tumour therapy in pediatrics

Yesterday I heard a talk at the Mainzer Medizinische Gesellschaft by Alexandra Russo from the university hospital in Mainz. She is responsible for treating children with cancer in that hospital. She talked about progress in cancer therapy for children, focussing on the situation in Germany. She did also mention international collaborations of her group in Mainz. A positive fact is that 80% of childhood cancers can be cured definitively. In other words the tumour can be eliminated in such a way that it does not return. This sounds much better than the situation for adults. A negative fact is that this percentage has not changed significantly in the last twenty years. Another negative fact is that among those people cured many have long-time side effects resulting from the chemotherapy they had. There was a group of former patients described who had had chemotherapy with a particular substance and many of these young people had hearing aids. Hearing loss is a known side effect of the drug they were treated with. The speaker is enthusiastic and optimistic about being able to change these things by applying personalized therapies. At the moment most treatments are still based on the classical methods: surgery, radiotherapy and chemotherapy. One special feature is that radiotherapy is not used in children under the age of three since the side effects would be too dramatic.

Some special features of treating children were mentioned. One is that it is often necessary to use drugs which are not approved for the treatment of children. There is a law in Germany that new drugs must be tested for their use in children as well as adults. However there are many exceptions to this based on the argument that the disease concerned does not occur in children. For instance children do not get lung cancer. The necessity of off-label use leads to problems with getting the drugs payed for and getting permission from an ethics commission. Even when these problems have been overcome in a given case there are still the problems that for children, due to lack of studies, the correct dosage and the safety profile are not known. The commercially available drugs are not suitable for use in children. For instance a single pill may contain a dose which is much too high for a small child. This means that the drugs must be specially processed by the clinic before they can be used. The speaker proudly showed a picture of a new machine they just got which is a 3-d printer for pills. It is still at the prototype stage but she expects it to bring them great benefits in the near future.

The speaker said that the amount of money spent on therapy in Germany is one of the highest in the world although not as much as in the US. In Britain only about half as much is spent. What is not so good is that much less sequencing is carried out in Germany than in many countries. So when she needs a lot of sequencing for her patients it can be difficult. A method for trying to improve the problems with the studies and approval would be to do studies linked not to a particular type of cancer cell but to a particular type of genetic defect. To make this possible sufficient genetic data about the patients must be obtained. She mentioned the example of Pembrolizumab, which was the first cancer drug to be approved for certain genetic situations rather a specific disease.

In the talk two examples of patients were discussed in some detail. The first was of a boy with a brain tumour who was six years old at diagnosis. It was first diagnosed as an astrocytome but this was later revised to glioblastome. A genetic irregularity was found which is best known from lung cancer. Then the idea was to try to use a drug which had worked in a lung cancer of this type to treat the brain tumour. An extra difficulty was to find a drug which would cross the blood-brain barrier. A drug was found and did have a positive effect. Unfortunately an infection of the patient meant that the treatment had to be discontinued for some time. This led to the tumour getting out of control and the death of the patient. Perhaps if the detailed genetic information had been available more quickly so that a good treatment could have been started more quickly the story would have had a better end. The second example was that of a nine-month baby with apparently swollen lymph nodes which turned out to have a tumour in the neck region. Despite different types of chemotherapy the tumour grew very much until it was acutely life-threatening. In looking for a targetted drug it was again important to have enough genetic information so as to see what signalling pathways were involved in the pathology. It turned out that the MAPK cascade was involved. (My attention is always drawn by the MAPK cascade since I did some work on mathematical models for it.) One way of obtaining information was to culture pieces of tumour in the presence of different drugs to see which ones might be helpful. In this case a suitable drug was found, a MEK inhibitor called cobimetinib. After three weeks treatment the size of the tumour had decreased by 94% and the child could live a relatively normal life. Unfortunately it looks as if the drug must be given indefinitely in order to control the tumour. At the moment the strategy is to try and reduce the dose so as to reduce the side effects.

I have a lot of admiration for someone doing a job like this. It involves intellectual challenges, emotional difficulties and the need for strong practical qualities. In any case, I found the talk fascinating.

Conference on mathematics and immunology in Blagoevgrad

I recently attended a conference on mathematics and immunology in Blagoevgrad in Bulgaria. I must admit that I knew very little about Bulgaria. I knew the name, I knew where it was and I knew that it had a Slavic language. That was about all. Thus it was educational for me to be in the country and also have the chance to talk to Bulgarians. It was in particular interesting to learn that there was a large Bulgarian empire centuries ago. I flew to Sofia and took a train south to the site of the conference. The train was quite old and slow but it passed through interesting countryside, some of which was extremely green and lush. I saw several Bee-eaters from the train. On the evening I arrived there were a lot of swallows flying around. They were flying quite high and fast and I was not able to identify them definitely. They looked and sounded different to the species I was familiar with. While they were eating mosquitos the mosquitos were eating me and that made it difficult to concentrate. A couple of days later I was able to convince myself that one suspicion I had had at the beginning was correct – they were Red-rumped Swallows.

The conference itself was small and I much prefer small and thematically focussed meetings such as this to large conferences. It was very pleasant to be among people who are interested in and knowledgeable about both mathematics and immunology. The first speaker was Becca Asquith who talked about KIRs, the inhibitory receptors found on natural killer cells. What I did not know before was that KIRs are also presented on T cells. It is well known that the susceptibility of individuals to infectious or auto-immune diseases is dependent on which MHC molecules they have. I was aware that, for instance, certain HLA-DR types are associated to an increased risk of multiple sclerosis. In fact HLA molecules may have positive or negative effects on disease risk. It turns out that the types of KIRs a given individual has can also have analogous effects. A central theme of the talk was how these statistically observed effects can be explained mechanistically and how mathematical models can help to distinguish between different mechanisms. A number of talks were related to epidemiology, considering in-host models, population models and the coupling of the two. One concerned a virus I did not know previously, the Usutu virus. Stanca Ciupe described modelling for experiments where house sparrows were exposed to mosquitos carrying this virus. The virus (and its name) originated in Africa but it has been spread to parts of Europe by migratory birds. Doing some more reading on the subject I discovered that it is reponsible for some cases where a lot of blackbirds have been seen to die. Humans can become infected with the virus but it does not seem to be directly harmful to us. The virus is nevertheless interesting as a candidate for one which might mutate and cause a serious disease of humans in the future. Jonathan Forde gave an interesting talk on the question of the best way to invest limited (financial or human) resources in fighting COVID-19 or other infectious diseases. Sometimes there is an optimal balance between vaccination and testing.

There were also talks on subjects other than infectious diseases. Vladimira Suvandjieva talked about some work she has done on modelling the role of NETs in lupus. Here mathematics is applied to a biological subject which I wrote about in this blog a long time ago. In this phenomenon the immune cells involved are neutrophils. Doron Levy talked about using mathematical models to better understand cancer immunotherapy. There were talks on the ways in which the time of administration can influence the effectiveness of chemotherapy against cancer and the strength of side effects. What is notable is a strong dependence on the sex of the patient. Apart from the science it was interesting to talk to the other participants from various parts of the world about political themes, thus being exposed to different facts and opinions. I have not had so many opportunities for this kind of conversation since the pandemic.

Fomites and backward bifurcations

I first met the curious word ‘fomite’ a few months ago. It means a carrier of infection which is not a human being or an animal. It evolved in an interesting way, as recounted in the Wikipedia article on this concept. It started out as the Latin word ‘fomes’. The plural of that is ‘fomites’, which was taken over into English. There it was interpreted as an English plural and gave rise to the corresponding singular ‘fomite’. Let me now get away from the word and consider the concept it designates. During the COVID-19 pandemic there was a lot of discussion about the modes of transmission of infection. In particular people wanted to understand the importance of the disinfection of surfaces (and of hands). These inanimate surfaces, where the virus might be present and act as a source of infection, are then (the surfaces of) fomites. As far as I can judge the consensus developed that this mode of transmission was not the key factor in the case of COVID-19 with attention being concentrated on aerosols. However important they may be in that particular case there is no doubt that there are diseases for which transmission by fomites is very important. The theme of hospital infections is a very important one these days and there fomites are likely to play a central role.

I came across the word fomite in the course of some research I did recently with Aytül Gökce and Burcu Gürbüz on some population models for infectious diseases. We just produced a preprint on that. One aspect of infection which was included in our model and which is not very common in the literature is that of infections coming from virus in the environment and here we can think of fomites. In modelling this phenomenon a choice has to be made of a function which describes the force of infection. We can consider an expression for the rate of infection of the from , where is the number of susceptibles and is the concentration of virus in the environment which may cause infection. What should we choose for the function ? This type of issue comes up in other modelling settings, in particular in those related to biology, where a choice of response function has to be made. In a biochemical reaction could describe the reaction rate as a function of the concentration of the substrate. Typical choices are the Michaelis-Menten function and the Hill function where is replaced in this expression by a power . The Michaelis-Menten function has a mechanistic basis, introduced by the people who it is now named after. Hill also presented a mechanistic basis for his function. It incorporates the phenomenon of cooperative binding, with the original example being the binding of oxygen to haemoglobin. Another example of the choice of response functions occurs in predator-prey models in ecology. Here describes the dependence of the rate of uptake of prey as a function of the density of prey. The functions which are mathematically identical to the Michaelis-Menten and Hill functions are called Holling type II and Holling type III. Holling gave mechanistic interpretations of these. Type II is associated with the fact that the predator needs some time to process prey and that that time is lost for the search for prey. Type III is associated with learning by the predator. In this list type I is missing. Type I refers to a linear function, except that to account for the fact that the rate of uptake of prey is in reality limited the linear function is usually cut off at some level, after which it is constant.

It seems that in epidemiology these issues have not been studied so much. There is an extended discussion of the subject in Chapter 10 of the book ‘Mathematical Epidemiology of Infectious Diseases’ by Diekmann and Heesterbeek. I mentioned this book in a previous post but unfortunately forgot to mention the names of the authors. At the beginning of the chapter it is stated clearly that it will not give a definitive answer to the questions it raises. I appreciate this kind of modesty. In that chapter there is a mechanistic derivation of a response function in a particular epidemiological setting. It is more complicated that the conventional ones and is not a rational function. The function corresponding to Holling type II has been been discussed in relation to epidemiology, apparently for the first time by Dietz. His discussion is purely phenomenological as opposed to mechanistic. In other words he chooses the simplest function satisfying some basic desired properties. In our paper we consider phenomenological models containing a power as in Holling type II () and Holling type III (). We found that the case gives rise to backward bifurcations while the case does not. Thus here the details of the response function can be of considerable mathematical or even medical importance. (The presence of backward bifurcations has implications for the strategy of therapies.) Another topic of the paper is the different ways in which imperfect vaccination can be described mathematically but I will not go any deeper into this theme here.

Biography of John D. Rockefeller by Ron Chernow

I have just read the biography ‘Titan’ of John D. Rockefeller by Ron Chernow. Rockefeller was a contemporary of Andrew Carnegie who I wrote about in a previous post, being just four years younger. Rockefeller became the richest man in the world after Carnegie had occupied that position. This book is a biography and not an autobiography and that is not an accident. While Carnegie had a talent and an inclination for writing and freely revealed many things about himself Rockefeller was extremely secretive. Given this it is surprising that so much is known about his life. At one time he gave extensive interviews to a journalist and Chernow was able to access the transcripts of these. He also engaged in a form of reverse engineering. Rockefeller wrote many letters but in doing so he tended to conceal the most important things. By contrast the writers of the letters he received were often less discrete and so Chernow could use those as a source of information about their recipient. Like Carnegie Rockefeller grew up in modest circumstances. However in another way his family background was very different. While Carnegie grew up in an atmosphere of honesty and hard work Rockefeller’s father ‘Big Bill’ was a swindler, quack doctor and bigamist. He used to abandon his wife and children for months at a time, although he did pay their bills when he returned after an unspecified length of time. The family frequently moved house due to the schemes of the father. It was very important for Rockefeller to achieve financial independence from his father. It was also important for him to fulfill moral standards which his father had violated. He was a dutiful father.

Rockefeller was very religious and his wife even more so. He belonged to the Baptist church and starting from a young age supported the church he went to with work, money and fundraising. He was strictly against drinking, smoking and even less obviously sinful things such as theatre and opera. The children were mostly confined at home, being taught by private tutors. The regime was very strict so that, for instance, a child who ate two pieces of cheese on one day received extensive reproaches. The mother stated that no woman needs more than two dresses. The children were encouraged to earn their own money. At a time when the family was already rich the parents concealed this fact from the children.

In his professional life Rockefeller was very civilized on the surface. On the other hand he was often very ruthless in secret. He usually observed the letter of the law although not always. On the other hand he did not hesitate to destroy the business of his competitors by all legal means when it suited him. Reading about these things reminded me of the methods of Bill Gates, which I read about in a biography some years ago. Rockefeller worked with all kinds of underhand tricks and perhaps he inherited this part of his character from his father. This means for me that I regard Rockefeller as a rather unpleasant character and in my judgment he is almost at the opposite pole from Carnegie. Rockefeller did not see his own acts as immoral, or at least he did not clearly admit it to himself. He believed that God was on his side and that he was working for good. In creating the monopoly of Standard Oil he believed he was working against the excessive instability of the oil market arising from unlimited competition. In his opinion he was not acting the way he did in order to become as rich as possible – his riches were just a byproduct of his doing the right thing. I find Rockefeller very strange character, with a complex mix of characteristics which I find positive or negative. There are aspects of his behaviour which I find admirable. There is the way in which he worked so consistently in order to achieve the things he believed in. There is his strict adherence to the religious principles which he believed to be valid. There is the fact that in a certain way he treated most people around him with respect. What I do not like is that he had little respect for science. He thought that a businessman should not waste his time with science since he could always hire a scientist if he needed one. His route to success and riches was through playing social games and I do not see that his professional activity led to technical advances, another contrast to Carnegie.

A well-known characteristic of Rockefeller is his philanthropy. He admired the corresponding activities of Carnegie but privately said that Carnegie was vain. He, Rockefeller, went to great lengths to stay in the background in the context of his philanthropic gifts. He generally did not want things named after him just because he had paid for them. He invested tremendous effort in trying to decide what were the most valuable causes he should contribute to. In this sense it seems that for him giving away money was more strenuous than earning it. Eventually, after the strain was damaging his health he delegated a lot of his philanthropic activity. An important principle of his was that he would only give money if it was matched by a certain sum raised for the same project from other sources. In the end he was often not too successful in implementing this policy – he was not able to stand up to the pressure from the beneficiaries. A good example of this were his huge contributions to the beginnings of University of Chicago. Rockefeller had a key influence on establishing medical research in the United States. He founded what is now called the Rockefeller University. He made a very important contribution to fighting hookworm in the southern US and later in other parts of the world. He himself believed in homeopathy but due to the fact that the people who managed his philanthropy were more enlightened than he was the money donated contributed essentially to establishing evidence-based medicine in the US and weakening the influence of homeopathy. Thus in a way he came to doing exactly the opposite of what his father had done.

This is a very high quality biography and contains a host of interesting things which I did not even mention.

Talks about malaria

I recently heard two talks about malaria at the Mainzer Medizinische Gesellschaft. The first, by Michael Schulte, was historical in nature and the main theme was the role of quinine as a treatment. The second, by Martin Dennebaum, was about malaria and its therapy today. Both talks were not only useful sources of information about malaria but also contained more general insights about medicine and its relations to society. In German the tree which is the natural source of quinine is called Chinarinde (i.e. China bark, in English it is called cinchona) and this had left me with the impression that the tree was from China. The first thing I learned from the first talk is that this is false. The tree comes from the Americas and was first used for medicinal purposes in Peru. A few weeks ago Eva and I visited a botanical garden in Frankfurt (Palmengarten) and saw a lot of those tropical plants which are the sources of things we are familiar with in everyday life (e.g. chocolate, cocoa, tobacco) and we in particular saw a cinchona tree. However I did not pay enough attention to realise its geographical origin at that time. There were men in Peru who had to cross a river to get to work and shivered a lot after they came out of the water. The idea came up that the bark of this tree could be used to reduce the shivering. At that time there were Jesuit missionaries in Peru. The Jesuits had been instructed by their leader Ignatius Loyola to bring back interesting things such as animals and plants from the exotic places they visited. One of the Jesuits in Peru, knowing that malaria is often accompanied by intense shivering, thought that cinchona bark might also help against malaria. This quite random analogy turned out to lead to a great success. Cinchona bark was sent to Rome and used there to treat malaria. It is remarkable how successfully this was done although the doctors knew nothing about the mechanisms at work in malaria. Without knowing about the existence of quinine they developed a way of extracting it very effectively using alcohol. They determined the right time to give the drug in the cycle of symptoms. In order for the treatment to be successful the drug must be given just after the infected red blood cells burst and the organisms are in the open in the blood and not protected. Quinine, the element of the cinchona bark most active against malaria was isolated around 1820. The first industrial production took place in Oppenheim, a town on the Rhein not far from Mainz. At one time Oppenheim was reponsible for 60 per cent of the world production of the substance. Malaria was a big public health problem in that region at the time and that was what stimulated the development of the industry. There is a story that the British colonists in India used to drink gin and tonic because tonic water contains quinine and thus provides protection against malaria. The speaker left it until the end of his talk to say that while the colonists did use quinine in other forms the concentration in tonic water is too low to be useful against malaria.

The second talk started with an interesting case history. A flight attendant flew from Frankfurt to Equatorial Guinea. Ten days after she got back she developed fever. Her husband had fever at that time due to influenza and she assumed she had the same thing. For this reason she did not seek medical advice until three days later. That was a public holiday and she was told she should come back the next day so that all the necessary tests could be done. The next day she landed as an emergency in the University Hospital in Mainz. A blood test showed that 25 per cent of her blood cells were infected with the organism causing malaria. The amount which is considered life-threatening is 5 per cent. The speaker said that if she had waited longer she would probably not have lived another day. Fortunately she did get there on time and could be cured. There are very effective drugs to treat malaria, namely those based on artemisinin. These drugs have their origin in traditional Chinese medicine. During the Vietnam war malaria was a big problem for those on both sides of the conflict. On the US side four or five times as many soldiers died of malaria than in combat. Both sides were looking for a drug to help with this problem and both looked to herbal sources, at first with little success. In the case of the Vietnamese they had enlisted the help of the Chinese to do this work for them. In China a secret ‘Project 523’ was set up for this purpose. As a part of this project Tu Youyou led the search for a malaria drug based on traditional Chinese medicine. She was successful and eventually got a Nobel Prize in 2015 for the discovery of artemisinin. From traditional literature she obtained a list of candidate plants and then subjected them to modern scientific analysis, in particular using experiments on mice. Her first attempts with the plant which produces artemisinin were not successful and it was another hint from ancient literature which helped her to overcome that difficulty. In fact the active substance was being destroyed by an extraction process at high temperature and once she had developed an alternative process at lower temperature positive results were obtained. Once the right candidate drug had been obtained the further analysis proceeded using all the tools of modern (non-alternative) medicine. I am no friend of ‘alternative medicine’ and I cannot help comparing the phrase to ‘alternative facts’. One of the things I have against ‘alternative medicine’ is that I think that if some part of it was really effective then it would quickly be adopted by real medicine and thus leave the alternative region. Nevertheless the story of artemisinin shows how in exceptional cases there can be a valuable flow information from traditional to real medicine and that this may require a great amount of effort. The type of malaria which is sometimes deadly is that caused by Plasmodium falciparum. Other types, caused by other Plasmodium species are less deadly but can become chronic. I think of novels where a typical figure was an army officer who suffered from malaria because he had served in India. From the talk I learned that the other types of malaria can be prevented from becoming chronic – it is just necessary to give the right treatment. To emphasize that malaria should be taken seriously in a country like Germany today he mentioned that at that moment there was again a malaria patient in intensive care in the University Hospital in Mainz although that case had not been so critical as that of the flight attendant.

Another paper on hepatitis C: absence of backward bifurcations

In a previous post I wrote about a paper by Alexis Nangue, myself and others on an in-host model for hepatitis C. In that context we were able to prove various things about the solutions of that model but there were many issues we were not able to investigate at that time. Recently Alexis visited Mainz for a month, funded by an IMU-Simons Foundation Africa Fellowship. In fact he had obtained the fellowship a long time ago but his visit was delayed repeatedly due to the pandemic. Now at last he was able to come. This visit gave us the opportunity to investigate the model from the first paper further and we have now written a second paper on the subject. In the first paper we showed that when the parameters satisfy a certain inequality every solution converges to a steady state as . It was left open, whether this is true for all choices of parameters. In the second paper we show that it is not: there are parameters for which periodic solutions exist. This is proved by demonstrating the presence of Hopf bifurcations. These are obtained by a perturbation argument starting from a simpler model. Unfortunately we could not decide analytically whether the periodic solutions are stable or unstable. Simulations indicate that they are stable at least in some cases.

Another question concerns the number of positive steady states. In the first paper we showed under a restriction on the parameters that there are at most three steady states. This has now been extended to all positive parameters. We also show that the number of steady states is even or odd according to the sign of , where is a basic reproductive ratio. It was left open, whether the number of steady states is ever greater than the minimum compatible with this parity condition. If there existed backward bifurcations (see here for the definition) it might be expected that there are cases with and two positive solutions. We proved that in fact this model does not admit backward bifurcations. It is known that a related model for HIV with therapy (Nonlin. Anal. RWA 17, 147) does admit backward bifurcations and it would be interesting to have an intuitive explanation for this difference.

In the first paper we made certain assumptions about the parameters in order to be able to make progress with proving things. In the second paper we drop these extra restrictions. It turns out that many of the statements proved in the first paper remain true. However there are also new phenomena. There is a new type of steady state on the boundary of the positive orthant and it is asymptotically stable. What might it mean biologically? In that case there are no uninfected cells and the state is maintained by infected cells dividing to produce new infected cells. This might represent an approximate description of a biological situation where almost all hepatocytes are infected.

Advances in the treatment of lung cancer

I enjoy going to meetings of the Mainzer Medizinische Gesellschaft [Mainz Medical Society] but they have have been in digital form for a long time now due to the pandemic. Recently I attended one of these (digital) events on the subject of the development of the treatment of lung cancer. There was a talk by Roland Buhl about general aspects of the treatment of lung cancer and one by Eric Roessner on surgery in lung cancer. Before going further I want to say something about my own relation to cancer. When I was a schoolchild my mother got cancer. In Orkney, where we lived, there was no specialist care available and for that reason my mother spent a lot of time in the nearest larger hospital, Foresterhill in Aberdeen. During my first year as a student in Aberdeen there was an extended period where I visited my mother in hospital once a week. I was not intellectually engaged in this issue and I do not even know what type of cancer my mother had. I seem to remember that at one point her spleen was removed, which suggests to me that it was a cancer of the immune system, lymphoma or leukemia. After some months my mother had reached the point where no useful further therapy was possible. She returned to Orkney and died a few months later. I must admit that at that time I was also not very emotionally involved and that I was not a big help to my mother in those troubled times for her. While I was a student I was friends with two other students, Lynn Drever and Sheila Noble. At one time I frequently heard them talking about a book called the ‘The Women’s Room’ by Marilyn French. I was curious to find out more but they did not seem keen to talk about the book. After the end of my studies I read the book myself. It is a feminist book and I think a good and interesting one. The reason I mention Marilyn French here is another good and interesting book she wrote. It is called ‘A Season in Hell’, which is a translation of the Rimbaud title ‘Une saison en enfer’. In the book she gives a vivid inside view of her own fight with a cancer of the oesophagus. After very aggressive treatments she was eventually cured of her cancer but the side effects had caused extensive damage to her body (collapse of the spine, kidney failure etc.). Parallel to the story of her own illness she portrays that of a friend who had lung cancer and died from it quite quickly. This book gave me essential insights into what cancer means, objectively and subjectively, and what lung cancer means. My own most intensive contact with cancer was in 2013 when my wife was diagnosed with colon cancer. I do not want to give any details here except the essential fact that she was cured by an operation and that the disease has shown no signs of returning. Motivated by this history I recently did something which I would probably otherwise not have done, namely to have a coloscopy. I believe that this is really a valuable examination for identifying and preventing colon cancer and that it was my responsibility to do it, although I was anxious about how it would be. In fact I found the examination and the preparations for it less unpleasant than I expected and it was nice to have a positive result. It is also nice to know that according to present recommendations I only need to repeat the examination ten years from now. A few years ago in the month of November my then secretary got a persistent cough. After some time she went to the doctor and was very soon diagnosed with lung cancer. She only survived until February. I attended a small meeting organised by her family in her memory and there I learned some more details of the way her disease progressed.

Now let me come back to the lectures. The first important message is nothing new: most cases of lung cancer are caused by smoking. Incidentally, the secretary I mentioned above smoked a lot when she was young but gave up smoking very many years ago. The message is: if you smoke then from the point of view of lung cancer it is good to stop. However it may not be enough. In the first lecture it was emphasized that the first step these days when treating lung cancer is to do a genetic analysis to look for particular mutations since this can help to decide what treatments have a chance of success. In the case of the secretary the doctors did look for mutations but unfortunately she belonged to the majority where there were no mutations which would have been favourable for her prognosis under a suitable treatment. In the most favourable cases there are possibilities available such as targeted therapies (e.g. kinase inhibitors) and immunotherapies. These lectures are intended to be kept understandable for a general audience and accordingly the speaker did not provide many details. This means that since I have spent time on these things in the past I did not learn very much from that lecture. The contents of the second lecture, on surgical techniques, were quite unfamiliar to me. The main theme was minimally invasive surgery which is used in about 30% of operations for lung cancer in Germany. It is rather restricted to specialized centres due to the special expertise and sophisticated technical equipment required. It was explained how a small potential tumour in the lung can be examined and removed. In general the tumour will be found by imaging techniques and the big problem in a operation is to find it physically. We saw a film where an anaesthetised patient is lying on an operating table while the huge arms of a mobile imaging device do a kind of dance around them. The whole thing looks very futuristic. After this dance the device knows where the tumour is. It then computes the path to be taken by a needle to reach the tumour from outside. A laser projects a red point on the skin where the needle is to be inserted. The surgeon puts the point of the needle there and then rotates it until another red point coincides with the other end. This fixes the correct direction and he can then insert the needle. At the end of the needle there is a microsurgical device which can be steered from a computer. Of course there is also a camera which provides a picture of the situation on the computer screen. The movements of the surgeon’s hands are translated into movements of the device at the end of the needle. These are scaled but also subject to noise filtering. In other words, if the surgeon’s hands shake the computer will filter it out. There is also a further refinement of this where a robot arm connected to the imagining device automatically inserts the needle in the right way. The result of all this technology is that, for instance, a single small metastasis in the lung can be removed very effectively. One of the most interesting things the surgeon said concerned the effects of the pandemic. One effect has been that people have been more reluctant to go to the doctor and that it has taken longer than it otherwise would have for lung cancer patients to go into hospital. The concrete effect of this on the work of the surgeon is that he sees that the tumours he has to treat are on average in a more advanced state than they were than before the pandemic. Putting this together with other facts leads to the following stark conclusion which it is worth to state clearly, even if it is sufficiently well known to anyone who is wiling to listen. The reluctance of people to get vaccinated against COVID-19 has led to a considerable increase in the number of people dying of cancer.