Mathematics of Emerging and Re-emerging Diseases

Mathematics of Emerging and Re-emerging Diseases Mathematics of Emerging and Re-emerging Diseases My recent research work focuses on two main themes. The first is the use of mathematical modeling approaches to gain insight into the effect of climate variables on the transmission and control of malaria (a major mosquito-borne disease that is endemic in over 100 countries). The second is the theoretical analysis of the systems of nonlinear equations associated with the mathematical modeling of the transmission dynamics of emerging and re-emerging diseases of public health importance. My work on malaria dynamics entails the design, analysis and simulations of novel weather-driven mathematical models, which typically take the form of compartmental systems of nonlinear differential equations, for studying the dynamics of both its vector (i.e., mosquito species) and the malaria disease. The main aim is to help provide insight on the expected effect of climate change (as measured in terms of changes in temperature and rainfall) on the global distribution of the vector and the disease burden. My work has provided insight into the central question on whether climate change will lead to a poleward expansion of malaria vectors (and cases) or a poleward-shift-with-no-net-expansion (of vectors and disease burden). I developed and analysed novel models for the effect of climate change on the population biology of the malaria mosquito, and used such models to estimate suitable temperature and rainfall ranges for maximum mosquito abundance in numerous endemic areas (thereby enabling us to suggest when control efforts should be implemented or intensified). For example, one of these studies showed that, for the KwaZulu-Natal province of South Africa, the peak mosquito abundance occurs when the mean monthly temperature and rainfall values lie in the range [22- 25]C and [98-121] mm, respectively. We have extended this work to determine suitable temperatures for maximum malaria transmission in various regions. My work on theoretical analysis of dynamical systems arising in mathematical epidemiology is focused on studying the asymptotic properties of the steady-solutions of these systems, as well as in characterizing the bifurcation types. These analyses enable the determination of important epidemiological thresholds, defined in terms of the parameters of the models, that govern the persistence and/or effective control (or elimination) of the disease being modeled. In other words, these analyses allow for the realistic assessment of the effectiveness of the control/intervention strategies in combatting the disease in the community. My work has focused on the determination of epidemiological processes or mechanisms that lead to the phenomenon of backward bifurcations in these models. This phenomenon, which entails the co-existence of multiple stable attractors when the reproduction number of the model is less than unity, has major consequences on the ability of existing interventions to effectively control the spread of the disease.