Application to pathogen evolution data

The interactions between the immunology within a host, the epidemiology in a population, and the evolution of the pathogen are too complex to be captured by traditional compartmental models68. Hence, there is a need to develop more advanced mathematical models, possibly hybrid systems, that allow a realistic study of infectious diseases dynamics where the immunity of the hosts is waning due to the evolution of the circulating pathogen. Combining different types of nonlinear equations, such as, partial, functional differential equations or integral equations within one system poses great challenges in their analysis, parameter estimation and their integration with data driven approaches.