Modeling Disease Dynamics at Within-Host and Between-Host Scales: HIV and Influenza as case studies

Mathematical models are becoming increasingly useful in studying the dynamics of infectious diseases, from within-host to between-host scales. With HIV and influenza as case studies, I will demonstrate how modeling can provide great insights into complex phenomena of these diseases. First, I will present a within-host model that can help address some of the issues related to the HIV-1 treatments in the face of drug resistance. Our model shows that although drug therapy cannot suppress the viral load due to resistance, it can alter the viral fitness resulting in an increase in CD4+ T cell (immune cell) count, which should yield clinical benefits. Furthermore, this benefit depends on the cell proliferation rate, which, in some situations, produces sustained T-cell oscillations. Second, using a between-host population model of avian influenza dynamics under periodic environmental conditions, I will discuss the effects of environmental temperature on the basic reproductive number, effective reproductive number, disease invasion threshold, and long-term disease persistence. Our results show that environmental variations predict several interesting features of avian influenza dynamics, which are observed in real data: peak-time variation, place-to-place variation, and seasonal double peaks (summer and fall).