New results on the asymptotic behavior of an SIS epidemiological model with quarantine strategy, stochastic transmission, and Lévy disturbance

Abstract

The spread of infectious diseases is a major challenge in our contemporary world, especially after the recent outbreak of Coronavirus disease 2019 (COVID‐19). The quarantine strategy is one of the important intervention measures to control the spread of an epidemic by greatly minimizing the likelihood of contact between infected and susceptible individuals. In this study, we analyze the impact of various stochastic disturbances on the epidemic dynamics during the quarantine period. For this purpose, we present an SIQS epidemic model that incorporates the stochastic transmission and the Lévy noise in order to simulate both small and massive perturbations. Under appropriate conditions, some interesting asymptotic properties are proved, namely, ergodicity, persistence in the mean, and extinction of the disease. The theoretical results show that the dynamics of the perturbed model are determined by parameters that are closely related to the stochastic noises. Our work improves many existing studies in the field of mathematical epidemiology and provides new techniques to predict and analyze the dynamic behavior of epidemics.

Acute threshold dynamics of an epidemic system with quarantine strategy driven by correlated white noises and Lévy jumps associated with infinite measure

“…Transmissible illness surveillance relies on analytical modeling and future forecasting as a key decision-making tool [ 1 ]. However, each illness is modeled and described by its own mode of transmission, so in each specific case, the selection of an appropriate method to adequately characterize disease dynamics is highly demanded [ 2 ]. In this regard, mathematical biology, especially through compartmental systems, is the most famous approach for obtaining an understandable view of the disease spread.…”

“…The above result can be proved using an analysis analogous to that of the proof of Lemma 2.2. in [ 2 ].…”

Probabilistic Analysis of a Marine Ecological System with Intense Variability

“…Water salinity, temperature, lighting, pressure, and human intervention are concrete examples of factors that influence ocean plankton dynamics. To mathematically portray this variability, sundry analytical methods have been used to educe facts and prophesy the future of the studied phenomenon [25][26][27][28][29][30][31][32]. The most well-known approach claims that external variations can be formulated by integrating the Wiener process into the associated formulation [23,24].…”

Long-term bifurcation and stochastic optimal control of a triple-delayed Ebola illness model with vaccination and quarantine strategies

“…and T (0) = I s (0) + I e (0) + I q (0) + I r (0). From Lemma 2.11. of [44], we infer that equation (2.2) is scientifically well-posed and the time average of its unique solution is estimated as follows:…”