On a SIS model with impulsive effects

TL;DR

This paper investigates a nonlinear SIS disease model incorporating impulsive culling effects, analyzing its positivity and stability without assuming normalized population transmission, thus providing insights into disease control strategies with impulsive interventions.

Contribution

It introduces a novel SIS model with impulsive effects and nonlinear incidence, analyzing stability and positivity without population normalization assumptions.

Findings

Positivity of the model is established.

Stability of both impulse-free and impulsive variants is analyzed.

Impulsive culling impacts disease dynamics significantly.

Abstract

This paper is concerned with a SIS (susceptible, infected and susceptible populations) propagation disease model with a nonlinear incidence rate and eventual impulsive (non- necessarily being simultaneous) culling of both populations. The disease transmission does not necessarily take into account the total population as a normalizing effect. In this sense, the considered model is a mixed pseudo-mass. The positivity, stability of both the impulse- free and impulsive under pulse culling variants of the model are investigated in this paper.