Archive for September, 2008

The complexity of tuberculosis

September 17, 2008

Among all the infectious diseases of humans those causing the most deaths at present (the so-called big three) are AIDS, tuberculosis and malaria. Tuberculosis is an illness which is not so present in the consciousness of inhabitants of the developed world since its main effects are in developing countries. It is important to realize that about 95 % of TB infections are latent (asymptomatic) and that they often become active after many years. About one third of the population of the world is infected with the pathogen Mycobacterium tuberculosis and this represents a massive silent health problem. For these figures and a general introduction to tuberculosis see the lectures of John McKinney at

McKinney points out two differences between tuberculosis and most other infectious diseases. One is that the relevant timescales for the epidemiology are much longer (many years rather than a few weeks). Another is that TB does not confer lasting immunity so that even if someone has completely recovered from the disease they can be affected by it again. He discusses this in the context of standard mathematical descriptions of epidemics such as the SEIR model mentioned in a previous post.

There is a vaccine against TB which has been around for the best part of a century, the BCG vaccine. McKinney gives a list of its good properties which few vaccines against any disease can compete with. Unfortunately it has a key weakness – it is very often ineffective. What exactly goes wrong does not seem to be understood but given the lack of lasting immunity under natural conditions it is not surprising that there is a problem. If a vaccine for TB almost always worked it would be making the human immune system react more effectively than it does in response to a real infection and this is a tall order.

Most cases of TB can be cured using antibiotics but the treatment is very demanding, combining several drugs and lasting several months. It is hard to ensure that patients finish the whole course of treatment and this is particularly difficult in the context of developing countries. Why is so difficult to combat M. tuberculosis using antibiotics? One reason seems to be that there are different populations of the bacterium and that any one drug is only effective against some of these populations. In his lectures McKinney discusses what might distinguish these populations. It is not enough to suppose that it only depends on the different niches available in the body. Even in an infection of a cell culture heterogeneity in the properties of the bacteria can be observed. If a particular drug is applied the time dependence of the population indicates the presence of more than one type of bacteria being killed at different rates. McKinney suggests that the explanation of this may require a stochastic component. Fluctuations in the state of individual bacteria may lead to some of them entering a dynamical process which takes them to another state. This may lead to populations of bacteria in two distinct states. Modelling this kind of behaviour requires something more sophisticated than the ODE of standard population dynamics.

Another interesting point mentioned by McKinney is the interaction between TB and AIDS. In one direction this is easy to understand. In the presence of AIDS the compromised immune system is not capable of controlling a latent TB infection and the disease is activated. The other direction is more mysterious. Apparently the presence of a TB infection speeds up the evolution of an HIV infection to the state where AIDS occurs.

Added note: a new TB vaccine which is a modification of the BCG vaccine has just started phase I clinical trials in humans. More information can be found in a press release of the Max Planck Society.

Fighting the hamburger disease

September 11, 2008

Today I heard a talk by Brett Finlay from the University of British Columbia at the Max Planck Institute for Infection Biology (MPIIB) which, as it turned out, had something called the ‘hamburger disease’ (which I had never heard of before) as one of its main themes. To describe the wider context let me recall that while the occurrence of E. coli in the human gut is usually not harmful and may even be beneficial due to its competition with bacteria whose effects are less pleasant, there are some special pathogenic strains of E. coli. Two of these are called EPEC (enteropathogenic E. coli) and EHEC (enterohaemorrhagic E. coli). The first of these causes diarrhoea in young children, mainly in developing countries. The second causes the hamburger disease to be discussed further below. It also involves diarrhoea but may have very serious complications. In particular this bacterium produces the Shiga toxin known from the bacterium of the genus Shigella which causes dysentery. These two strains were two of the main protagonists in the talk along with a bacterium Citrobacter rodentium naturally occurring in mice with analogous properties. The last organism provides a useful animal model for studying EPEC and EHEC.

The EHEC bacterium affects cattle. The cattle do not get seriously ill but they spread the bacterium. During slaughtering it can happen that the meat gets infected with the bacteria. As an example hamburgers can be affected leading to outbreaks of disease among humans. This kind of incident explains the name ‘hamburger disease’. Since the cause is known it is possible to test meat for infection. If an infection in found in one place in a large delivery all the meat will be rejected for human consumption due to the health risk. This can be a very costly affair. Hence producers of meat and hamburgers have a strong financial motivation to solve this problem.

Finlay had the idea of vaccinating the cattle. At first sight this does not seem reasonable – after all the cattle do not mind the disease. It does, however, prevent the spread of the bacteria and thus can solve the problem. Using the insights gained from basic research it was possible to produce a cost-effective vaccine rather rapidly. There were some problems of a more political nature to be solved. Who pays for the vaccine? Should it be approved by authorities for human or animal health? It seems that these have been solved satisfactorily. The vaccine now has official approval in Canada and is expected to get approval in the US soon.

In the course of his description of the development of the vaccine the speaker said something like ‘At this point the mathematicians come in’. He said it in such a way that he obviously expected his audience to know exactly what he meant. I did not and unfortunately I did not have an opportunity to ask him. Did he mean some kind of statistics, or some kind of model for the population dynamics of the bacterium, or something quite different? I do not know.

Mosquito bites

September 10, 2008

I recently returned from a stay in the south of France where I had more contact with mosquitos than I would have liked. During a visit to Arles I was beset with extreme itching of my left upper arm. It was as if a long needle had been inserted, with the difference that the result was itch rather than pain. This led me to wonder about the mechanisms resulting from a mosquito bite. The only bites on the part affected were at least two days old and had had no consequences of comparable intensity prior to that. I am familiar enough with the coming and going of the swelling due to mosquito bites collected in the garden at home. I have, however, never carefully observed the course of events or tried to find out what is known about how it works. On that day I decided that the time had come and that I should consult the internet and other sources. I had read that the mosquito injects some kind of anaesthetic but I knew no more than that. I was afraid that these phenomena, while so irritating, might have been considered of too little importance to be studied seriously.

Looking at what is on the internet and books I have at home provided some information but I did not find a comprehensive account to satisfy my curiosity. Some things I did find are as follows. Local allergic reactions are often associated with the production of immunoglobulins of type IgE and the activation of mast cells. The mast cells release substances contained in their granules and this causes an immediate reaction. Substances they produce later lead to the activation of white blood cells such as eosinophils and this may well be what causes a second phase of itching and swelling. Some questions remain. Is it an observational fact that a single bite leads to at most two phases of itching (and not three, for instance)? Perhaps I can do some field work on that point. If the mosquito saliva produces an allergic reaction when injected into to the blood why does it not, at least in the vast majority of cases, produce something really bad like an anaphylactic shock? Something I did not find anywhere is what the substances in the mosquito saliva are which lead to the itching. Presumably they affect certain nerves. I wonder if the mechanism of this is understood.


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