Theoretical studies on a two strain model of drug resistance: understand, predict and control the emergence of drug resistance

Infectious diseases are a leading cause of death worldwide. With the development of drugs, vaccines and antibiotics, it was believed that for the first time in human history diseases would no longer be a major cause of mortality. Newly emerging diseases, re-emerging diseases and the emergence of microorganisms resistant to existing treatment have forced us to re-evaluate our optimistic perspective. In this study, a simple mathematical framework for super-infection is considered in order to explore the transmission dynamics of drug-resistance. Through its theoretical analysis, we identify the conditions necessary for the coexistence between sensitive strains and drug-resistant strains. Farther, in order to investigate the effectiveness of control measures, the model is extended so as to include vaccination and treatment. The impact that these preventive and control measures may have on its disease dynamics is evaluated. Theoretical results being confirmed via numerical simulations. Our theoretical results on two-strain drug-resistance models are applied in the context of Malaria, antimalarial drugs, and the administration of a possible partially effective vaccine. The objective is to develop a monitoring epidemiological framework that help evaluate the impact of antimalarial drugs and partially-effective vaccine in reducing the disease burden at the population level. Optimal control theory is applied in the context of this framework in order to assess the impact of time dependent cost-effective treatment efforts. It is shown that cost-effective combinations of treatment efforts depend on the population size, cost of implementing treatment controls, and the parameters of the model. We use these results to identify optimal control strategies for several scenarios.