Asymptotic extinction and persistence of a perturbed epidemic model with different intervention measures and standard Lévy jumps

Abstract

Controlling an outbreak through response measures is critical to saving lives and protecting vulnerable populations. This article proposes an epidemic model with three intervention measures: media coverage, isolation, and medical therapy. Since randomness plays an important role in biology, from the molecular level to the organismal level, we extend our system to a more realistic framework, which then takes into account the effect of standard jumps due to some sudden environmental changes. After providing the associated framework, the sharp criteria for asymptotic extinction and persistence of illness are derived. To check the accuracy of our results, we perform two numerical examples.