Stochastic Epidemic Model for COVID-19 Transmission under Intervention Strategies in China

Abstract

In this paper, we discuss an EIQJR model with stochastic perturbation. First, a globally positive solution of the proposed model has been discussed. In addition, the global asymptotic stability and exponential mean-square stability of the disease-free equilibrium have been proven under suitable conditions for our model. This means that the disease will die over time. We investigate the asymptotic behavior around the endemic equilibrium of the deterministic model to show when the disease will prevail. Constructing a suitable Lyapunov functional method is crucial to our investigation. Parameter estimations and numerical simulations are performed to depict the transmission process of COVID-19 pandemic in China and to support analytical results.

A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein–Uhlenbeck process: dynamics analysis

“…Indeed, since the continuous spectrum of environmental noise, many parameters involved in infectious disease systems, such as transmission rates, mortality rates and so on, should fluctuate randomly around their mean [9][10][11][12][13][14][15]. Zhang et al [8] pointed out there are two methods to perturb parameters in the literature, one is linear Gaussian white noise [14,15] and the other is the meanreverting Ornstein-Uhlenbeck process. But for the parameter perturbation in the Gaussian white noise mode, the variance goes to infinity if the time goes to zero, which is unreasonable.…”

Attention based parameter estimation and states forecasting of COVID-19 pandemic using modified SIQRD Model

“…The parameters of these mathematical models capture the global behavior of the trajectories of epidemic numbers, which may be inferred or interpreted as the behavior of the population in terms of mobility [20] , as well as transmitability of virus [31] that may lead to the implementation of measures [21] like social distancing, quarantine management, mandatary mask wearing and closing of public and private places. In literature, these parameters are either assumed, or estimated through optimization techniques from the domain of nature-inspired algorithms [23] , Bayesian algorithms [32] and gradient-based algorithms [33] , in application of fitting the real world data over differential system [34] , basis functions [35] , spline fitting [36] , Kalman filter [37] , neural nets [38] and even recurrent nets [33] .…”

“…In literature, these parameters are either assumed, or estimated through optimization techniques from the domain of nature-inspired algorithms [23] , Bayesian algorithms [32] and gradient-based algorithms [33] , in application of fitting the real world data over differential system [34] , basis functions [35] , spline fitting [36] , Kalman filter [37] , neural nets [38] and even recurrent nets [33] . Furthermore, stochastic [31] or smooth [36] perturbations in the parameters of these models have been studied that lead to the better fitting of the epidemic models over real-world data. Not only this but these parameter variations have been studied to be essential, as the fluctuations in infection-related parameters were found to be linked with the stability of infected curves [31] .…”

“…Furthermore, stochastic [31] or smooth [36] perturbations in the parameters of these models have been studied that lead to the better fitting of the epidemic models over real-world data. Not only this but these parameter variations have been studied to be essential, as the fluctuations in infection-related parameters were found to be linked with the stability of infected curves [31] .…”