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.
