A Spatially Dependent Vaccination Model with Therapeutic Impact and Non-linear Incidence

Abstract

This study presents a spatially dependent vaccination model considering therapeutic impact with non-linear incidence rate where the spatial habitat is a subset of \( \mathbb {R}^{n} \) with smooth boundary. Auxiliary results such as disease-free and disease equilibrium states’ basic reproduction number are calculated. This study also includes both local and global stability constraints, uniform persistence condition and existence of the unique solution of the model. Our study showed that the global stability of the model depends on the threshold level \( \mathcal {R}_{0} \) in the way that \( \mathcal {R}_{0} \le 1 \) refers to disease-free equilibrium \( E_{0} \) where \( \mathcal {R}_{0} > 1 \) indicates unique disease equilibrium \( E^{*} \).