An immunity-structured SEIRS epidemic model with variable infectivity and spatial heterogeneity

A mathematical model is proposed for the spread of an epidemic disease agedependent infectivity through asexual population with spatial heterogeneity, assuming that some individuals recover from temporary immunity, another part permanent and last no immunity. The demographic changes such as births deaths due to natural causes chronological age are not taken into account. based on a system partial integro-differential equations including differential equation describe evolution who have recovered existence uniqueness globally defined solution proved, its long-time behaviour studied.