Abstract:
Disease dynamics are inherently influenced by the interplay between hosts and parasites. And this interaction may be subject to demographic and environmental variability. As environmental conditions shift and human interventions evolve, understanding these dynamics is crucial for effective disease management. This thesis investigates into the wide area of disease modelling, with a particular emphasis on the impact of external variability and stochasticity on epidemic dynamics within the context of host-parasite. First, we investigate the global stability dynamics and sensitivity of COVID- 19 transmission models considering timely and delayed diagnosis. Through theoretical analysis and numerical simulations, we show that the disease persistence depends on the basic reproduction number, R0. Our results suggest reducing the inflow of new individuals into the country or ensuring early diagnosis will lower the basic reproduction number and thereby limiting secondary infections and preventing multiple epidemic peaks. Next, we study the impact of imperfect vaccines, vaccine trade-offs, and population turnover on infectious disease dynamics. Using a mathematical model, we compute the basic reproduction number, establish global stability conditions of equilibria and perform sensitivity analysis. We derive conditions for the vaccination coverage and efficiency to achieve disease eradication assuming different intensity of the population turnover (weak and strong), vaccine properties (transmission and/or recovery) and trade-off between the latter. We show that the minimum vaccination coverage increases with lower population turnover, decreases with higher vaccine efficiency (transmission or recovery), and is increased/decreased by up to 15% depending on the vaccine trade-off. We then formulate a stochastic model for disease transmission in heterogeneous populations of vaccinated and unvaccinated hosts. We prove the existence of a unique nonnegative weak solution and derive conditions for extinction and persistence in mean. Simulations illustrate how demographic variability can alter vaccination outcomes and long-term disease persistence. Finally, we outline future research on metapopulation models for malaria forecasting, incorporating temperature variability and some vaccination strategies to account for climate-sensitive transmission regarding a specific vaccine. This extension aims to enhance predictive accuracy and support targeted interventions for malaria control in a changing climate.
