Modeling the emergence of multi-drug resistant TB hot zones

Rebecca Freeman submitted this essay for the Evolution class.

According to the World Health Organization (WHO), a “hot zone” is an area with >5% prevalence (or incidence) of Multi-Drug Resistant Tuberculosis (MDRtb). Sally M Blower and Tom Chou have been using a mathematical method to track the emergence and evolution of multiple strains of drug resistant tuberculosis, but they have now developed a new, more complex mathematical model. Before this model, there was only a two strain model, meaning it was only relevant to individuals that can be infected with a wild type pansensitive strain or a drug resistant strain, but there are many more strains then this. There are a resistant strains only to one drug and some resistant to multiple drugs. This means there is a multitude of strains in these hot zones and there was a need for a better way to track this (Blower and Chou 2004). Blower and Chou realized that a more complex mathematical model is necessary to capture the complexity of the epidemiology of the hot zones, and the evolution of hot zones was very unclear

Understanding drug resistance is important to understanding the, and Blower and Chou explain the evolving of resistance very well. They give three processes that are involved in generating drug resistance: Transmission of drug resistant strains to uninfected individuals, which is transmitted resistance; Conversion of wild pansensitive cases to drug resistant cases, which is acquired resistance; finally, cases where they have drug resistant strains and it becomes resistant to more antibiotics during treatment, which is amplified resistance. What everyone has had to do in the past is just study acquired and transmitted resistance, and now with the new model, they can incorporate amplification resistance. This was a big problem because it has been shown that inadequate treatment of DRtb can result in the amplification of drug resistant strains, which may be an important process of MDR epidemics (Blower and Chou 2004). So this is where Blower and Chou came in. They created a model, the call the amplifier model, that enables the tracking of emergence and evolution of MDR strains, the transmission of these strains and the amplification of these strains during repeated episodes of treatment.

Blower and Chou are really studying the effects of inadequate treatment programs, and how this may lead to a higher prevalence in MDRtb. One problem that this research cannot completely take into account yet is the transmittance ability of MDRtb compared to pansensitive tuberculosis. This is an area that is hazy right now, and so this cannot completely be incorporated into the model. Amazingly, they have measured a general fitness of MDRtb vs. pansensitive tuberculosis, by calculating the treatment fail rates and treatment cure rates of the each category of strains.

The authors were very clear with the purpose of the model. Even though the mathematical model is very complex, the idea and how they explain it is easily understandable. They use R0 to stand for the average number of secondary cases caused by one infectious case in a population where treatments are available. Their model breaks this up into four categories of strains: The wild type pansensitive [R0(1)], which is sensitive to all drugs; Pre-MDR [R0(2)], which is sensitive to one of the main drugs used to treat tuberculosis; MDR [R0(3)], which is resistant to both of the main treatment drugs; and post-MDR [R0(4)], which is resistant to both of the main antibiotics and others as well (Blower and Chou 2004). With the information gathered from over 30 years of date they constructed likely evolutionary trajectories of hot zones, and with this they also took into account low cure rates vs. high amplification probabilities in many areas. They also tried to incorporate which strains are more transmissible, but as I said before this was not really possible with their model and there was a large degree of uncertainty.

The results of their model matched the WHO predictions well, but there were some distinct differences, and I think these differences are what make this research so important. By using all for types (R01-4) they found great variability in incidence and prevalence. When treatments were originally started strains of pre-MDR strains emerged quickly, so incidence and prevalence of pre-MDR strains increased, and this subsequently led to possible amplification of resistance and MDRtb epidemics in certain areas. The question is: Why certain areas and not others? This question is explained by Blower and Chou. Interestingly, areas with bad treatment programs do not necessarily have a really high incidence of MDRtb, it has stayed pretty steady at a 5%-14% (Blower and Chou 2004). This to me seems like an argument that MDRtb is not as easily transmissible, because its rates overall have stayed pretty low, but there was no significant evidence for this. The WHO predictions state that a >5% prevalence OR incidence in MDRtb equals a hot zone. Blower and Chou found the mathematical relationship between MDR prevalence and incidence. MDR prevalence can be three times greater then MDR incidence. They used the results to evaluate the hot zones on prevalence or incidence. If it is by incidence then only 20% of those areas would be considered hot zones and 51% if criterion is prevalence (Blower and Chou 2004). I see this as an argument for the fitness of MDRtb to be very high and transmissible ability to be lower, because there are less new cases, and more cases that have just become more resistant.

When looking at the four strains the hot zones had a much lower R0 for pansensitive strains (median=.82), which suggests that the wild type strain should be slowly eradicated. The R0 for the pansensitive strains in non-hot zones were all above 1 (median=1.39) Looking at the rate of detection of cases and treatment rates in hot zones versus non-hot zones it is 55% to 25% (Blower and Chou 2004). This shows that places where they have control programs were successful at fighting pansensitive strains but ironically it created more MDRtb strains, making it more likely to become a hot zone.

The importance of this research is that they have figured out that the difference between incidence and prevalence rates is significant enough to change the view of an area as being a hot zone or not. Their research looks at many factors that go into the evolution of these hot zones. Out of the many factors they actually saw that case detection and treatment rates were the most important factors. They came to this conclusion because if case detection and treatment rates were low, and the amplification was high, it still did not generate a hot zone. Vise versa, if the case detection and treatment rates were high and the amplification rates were low; it was likely to become a hot zone. The point is that these areas with high case detection and treatment rates should not increase these rates unless high cure rates are achieved first. Blower and Chou have created a model that has multiple dimensions and can help the WHO in the future to prevent hot zones from popping up in high risk regions. The WHO already had a model for this but it was nowhere complex enough to correctly calculate prevalence and incidence of MDRtb, and how their mathematical relationship.

Reference:

Sally M Blower, Tom Chou (2004). Modeling the emergence of the 'hot zones': tuberculosis and the amplification dynamics of drug resistance Nature Medicine, 10 (10), 1111-1116 DOI: 10.1038/nm1102