Math Biology Seminar: Jummy Funke David

Different mathematical models (direct and indirect transmission models) were used to understand and analyze different infectious diseases dynamics and possible prevention and/or elimination strategies. As a first step, an age of infection model with heterogeneous mixing and indirect transmission was considered. The simplest form of SIRP epidemic model was introduced and served as a basis for other models. Most mathematical results in this part were based on the basic reproduction number and the final size relation. The epidemic model was further extended to incorporate the effect of diffusion and how the coupled PDE-ODE system could be reduced to an ODE system with a diffusion term. A novel approach to modeling air-transmitted diseases using an ODE system was proposed, and showed how the reduced ODE system approximates the coupled PDE-ODE system. In addition, a deterministic compartmental model of the co-interaction of HIV and infectious syphilis transmission (direct transmission) among gay, bisexual and other men who have sex with men (gbMSM) was developed and used to examine the impact of syphilis infection on the HIV epidemic, and vice versa. Analytical expressions for the reproduction number and necessary conditions under which disease-free and endemic equilibria are asymptotically stable were established. Numerical simulations were performed and used to support the analytical results. Finally, the co-interaction model was modified to assess the impact of combining different HIV and syphilis interventions on HIV incidence, HIV prevalence, syphilis incidence and all-cause mortality among gbMSM in British Columbia from 2019 to 2028. Plausible strategies for the elimination of both diseases were evaluated. According to our model predictions and based on the World Health Organization (WHO) threshold for disease elimination, we suggested the most effective strategies to eradicate the HIV and syphilis epidemics over a 10-year intervention period. The results of the research suggest diverse ways in which infectious diseases could be modeled, and possible ways to improve the health of individuals and reduce the overall disease burden, ultimately resulting in improved epidemic control.