Structure Preserving Splitting Techniques for Ebola Reaction–Diffusion Epidemic System

In this paper, we deal with the numerical solution of the reaction–diffusion Ebola epidemic model. The diffusion which is an important phenomenon for the epidemic model is included in the model. This inclusion has made the model more comprehensive for studying the disease dynamics in the human population. The quantities linked with the model indicate the population sizes which are taken as absolute, therefore, the numerical schemes utilized to solve the underlying Ebola epidemic system should sustain the positivity. The numerical approaches used to solve the underlying epidemic models are explicit nonstandard finite difference operator splitting (ENSFD-OS) and implicit nonstandard finite difference operator splitting (INSFD-OS) techniques. These schemes preserve all the physical features of the state variables, i.e. projected schemes hold the positive solution acquired by the Ebola diffusive epidemic model. The underlying epidemic model illustrates two stable steady states, a virus-free state, and a virus existence state. The suggested approaches retain the stability of each of the steady states possessed by the assumed epidemic model. A numerical example and simulations for validation of all the characteristics of suggested techniques are also investigated.