Modeling the dynamics of the SARS-CoV-2 virus in a population with asymptomatic and symptomatic infected individuals and vaccination

Abstract

The SARS-CoV-2 virus remains a pressing issue with unpredictable characteristics. The pandemic has spread worldwide through human interactions. Since the nature of the disease differs everywhere and it has a stochastic effect, we therefore develop a stochastic mathematical model to investigate its temporal dynamics. Asymptomatic individuals have a major effect on the spreading dynamics of the SARS-CoV-2 virus therefore, we divide the total population into susceptible, asymptomatic, symptomatic, and recovered groups. Multiple vaccinations have commenced across the globe. In this study, we assume that the vaccine confers permanent immunity. Moreover, due to the unpredictable characteristics of the disease random fluctuations are assumed in every population group. Using this model we show the existence and uniqueness of positive solutions to the proposed problem. We also discuss the disease extinction and persistence in the model to depict how contagious diseases can be eliminated from the community. We use the real data of SARS-CoV-2 virus, reported in Oman from the 1st January 2021 to 23rd May 2021 to parameterize the model. We then perform large-scale computational analysis to show the numerical simulation and verify the analytical findings.

Risk-based cost-benefit analysis of alternative vaccines against COVID-19 in Brazil: Coronavac vs. Astrazeneca vs. Pfizer

“…Many mathematical models have been proposed to describe the dynamics of the COVID-19 pandemic under mass vaccination programs. We found that both deterministic [1] , [21] , [22] ; Tran Kiem et al [24] , [28] ,MacIntyre et al [31] ) and stochastic [23] , [35] models are addressed. These studies provided significant results and relevant contributions to public health management.…”

A Study on the Fractal-Fractional Epidemic Probability-Based Model of SARS-CoV-2 Virus along with the Taylor Operational Matrix Method for Its Caputo Version

“…Khan et al [59,60] modeled a mathematical structure of dynamics of SARS-CoV-2 virus in the form of four initial value problems equipped with four state functions S, P 1 , P 2 , and R, which are a part of total population. This model is…”

“…As a first visualization, in Figure 1, we demonstrate the real data versus present model simulation. Then, behaviors of four subclasses are presented in Figures 2(a)-2(d) with the chosen initial values S = 100, P 1 = 90, P 2 = 80, and R = 70, respectively, and under various fractal-fractional orders ω and v. Now, we simulate and discuss the dynamics of the model based on the parameters provided by [60]. Based on this source, we assume Θ = 30, r = 0:003, s = 0:05, b = 0:05, b 1 = 0:05, p = 0:4, b 2 = 0:04, r 1 = 0:05, q = 0:2, b 3 = 0:6, and r 2 = 0:6.…”

Breakdown of a Nonlinear Stochastic Nipah Virus Epidemic Models through Efficient Numerical Methods

“…Probability Space [ 33 ]: A probability space is a three-tuple , , in which the three components are: Sample space: A nonempty set called the sample space , which represents all possible outcomes; Event space: A collection of subsets of called the event space . If is discrete, then usually .…”