Dynamics of Delayed Systems with Applications to Ecoepidemiology

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Ecoepidemiology is the study of interacting species in which diseases spread. Theoretical research and field observations have established the prevalence of various infectious diseases amongst the majority of ecosystem populations. This has necessitated the study of the impact of epidemiological parameters in the ecological domain. On the other hand, delay is very common in many processes such as population dynamics and epidemiology. Unfortunately, not much has been done for delayed ecoepidemic models. This motivates the proposed research. In this project, some new delayed ecoepidemic models will be proposed. With existing and these newly built delayed ecoepidemic models as prototypes, we will study the local and global dynamics of some abstract delayed equations. In these equations, delay can be discrete, distributed, or state-dependent. We concern with the stability of equilibria, Hopf bifurcation, backward bifurcation, spreading speed, and travelling waves. Techniques like linearization, Lyapunov functional method, normal form theory, monotone operator theory will be employed. This will contribute greatly to the theory of delayed differential equations. Moreover, the theoretic results will be applied to concrete problems. We hope that the obtained results will be useful to guide public health policy decisions and to control infectious diseases.