High order discretization methods for spatial-dependent epidemic models

In this paper, an epidemic model with spatial dependence is studied and results regarding its stability numerical approximation are presented. We consider a generalization of the original Kermack McKendrick in which size populations differs space. The use local yields system partial-differential equations integral terms. uniqueness qualitative properties continuous analyzed. Furthermore, different temporal discretizations employed, step-size restrictions for discrete model's positivity, monotonicity preservation, population conservation investigated. provide sufficient conditions under high-order schemes preserve computational process sufficiently accurate approximations. Computational experiments verify convergence accuracy methods.