A Numerical and Analytical Study of a Stochastic Epidemic SIR Model in the Light of White Noise

Abstract

This study examines a novel SIR epidemic model that takes into account the impact of environmental white noise. According to the study, white noise has a significant impact on the disease. First, we establish the solution’s existence and uniqueness. Following that, we explain that the stochastic basic production ${\mathfrak{R}}_0$ is a threshold that determines the extinction or persistence of the disease. When noise levels are high, we acquire ${\mathfrak{R}}_0<1$ , which causes the sickness to disappear. A sufficient condition for the existence of a stationary distribution is archived when the noise intensity is high, which suggests the infection is prevalent when ${\mathfrak{R}}_0>1$ . Finally, numerical simulations are used to explain the key findings.