Mathematical Modeling of Malaria: Theories of Malaria Elimination
Columbia University. International and Public Affairs
Columbia University. Microbiology and Immunology
Columbia University. Medicine
Columbia University. Sustainable Development
This dissertation describes the development and application of a new mathematical model for simulating the progression of Plasmodium falciparum infections in individuals with no malarial acquired immunity. The model allows for stochastic simulation of asexual and sexual parasitemias as well as the onset of fever and human to mosquito infectivity on a daily time scale. The model components for the asexual and sexual stages were developed elsewhere but are here extended to allow for simulation of the full range of dynamics observed in a subset of malaria therapy patients. As a first application of the model, I calculate the human component of malarial R0, the basic reproductive number. I then compare this value to those from three other models and describe how this quantity can be used to model malaria transmission. The second application of the model incorporates the effects of drug treatment on progression of infection by utilizing modeled pharmacokinetic and pharmacodynamic properties of a variety of antimalarials. I utilize a stage specific proportional killing model for sexual stages, informed from recent in vitro data. The relationship of effect sizes to treatment coverage and type of treatment in both early and late treatment seeking settings is calculated. In the third chapter, I consider the economic and epidemiological ramifications of antimalarial and rapid diagnostic subsidization for malaria control. For the epidemiological modeling I utilize a semi-mechanistic model of the spread of drug resistance parameterized from historical malaria mortality data; for the economic model I consider the effect of rapid diagnostics on the intensive and extensive margins of antibiotics and antimalarials, as well as the benefits to improved targeting of both. I find that rapid diagnostic testing is justified given our baseline assumptions for areas with low proportions of malarious individuals among all treatment-seekers, but that caution is necessary before deployment worldwide. For antimalarial subsidization, we find that this is a cost-effective method for reducing mortality in developing countries, though efforts to delay the onset and slow the spread of resistance are urgently needed.
Ph.D., Columbia University.
2012-08-23 10:58:18 -0400
2012-08-23 11:07:40 -0400