The threshold of a deterministic and a stochastic SIQS epidemic model with varying total population size

Abstract

Highlights A new a deterministic and stochastic epidemic model with varying total population size is proposed. The thresholds of the deterministic and stochastic epidemic model are established respectively. Our methods can improve some existing results. We carry out numerical and find a critical isolation rate 0.0217. The empirical probability density are presented.

Global dynamics of a network-based SIQS epidemic model with nonmonotone incidence rate

“…How to propose effective measures of disease control is an important research theme for the complex network infectious diseases. Quarantine of symptomatic individuals is an intervention program for controlling the propagation of infectious diseases, and this method has been used to prevent diseases such as cholera and COVID-19 [18] , [19] , [20] , [21] , [22] . The most direct method of controlling the transmission of epidemic may be the quarantine of infected persons, because it disrupts the links that connect the infected persons to the susceptible persons.…”

Dynamics and optimal control of a stochastic coronavirus (COVID-19) epidemic model with diffusion

“…Sun et al [ 21 ] proposed an SEIQR model in light of the influences of lockdown and medical resources on the propagation of COVID-19. Zhang et al [ 22 ] considered the threshold of a stochastic SIQS epidemic model with varying total population and its corresponding deterministic epidemic model. Zhang et al [ 23 ] constructed a SIQRS model on networks and investigate the related optimal control problems.…”

Threshold dynamics for a class of stochastic SIRS epidemic models with nonlinear incidence and Markovian switching

“…Recently, many classes of stochastic epidemic models have been proposed and studied (see for example, [3,5,8,22,24,30,31,33,35]). In addition, stochastic models give a real vision, analysis and modelization of infectious diseases compared with the deterministic counterparts [21,37,42].…”