Abstract
In this paper, we formulate an SVITR deterministic model and extend it to a stochastic model by introducing intensity of stochastic factors and Brownian motion. Our basic qualitative analysis of both models includes the positivity of the solution, invariant region, disease-free equilibrium point, basic reproduction number, local and global stability of disease-free equilibrium point, endemic equilibrium point, and sensitivity. We obtain the stochastic reproduction number and local stability by using twice differentiable Itô’s formula. We prove the global stability of the disease-free equilibrium point by using a Lyapunov function. We determine the sensitivity of the effect of each parameter on basic reproduction number of the model by using a normalized sensitivity index formula. On the other hand, we demonstrate numerical simulation results of deterministic and stochastic models of COVID-19 by using Maple 18 and MATLAB software. Our simulation results indicate that reducing the contact between infected and susceptible individuals and improvement of treatment play a vital role in COVID-19 pandemic control.
Highlights
Mathematical modeling is useful in understanding and analyzing the behavior of infectious disease transmission dynamics in humans and animals
Corona Virus Disease 2019 (COVID-19) is an infectious disease caused by Sever Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2)
Our model is governed by the following assumptions: All parameters are nonnegative, the total population size is constant, vaccination is introduced to the susceptible individuals, susceptible individuals are recruited by birth or immigration, the treated individuals cannot transmit COVID-19 disease to the susceptible population, and by losing temporary immunity the recovered individuals become susceptible again
Summary
Mathematical modeling is useful in understanding and analyzing the behavior of infectious disease transmission dynamics in humans and animals. Tang et al [17] proposed a deterministic compartmental model incorporating the clinical progression of the disease, the individual epidemiological status, and the intervention measures They found that the control reproductive number could be as high as 6.47, and those intervention strategies such as intensive contact tracing followed by quarantine and isolation can effectively reduce the control reproduction number and the transmission risk. Imai et al [8] conducted computational modeling of potential epidemic trajectories to estimate the size of the disease outbreak in Wuhan, with a focus on the human-to-human transmission. Isolation of an infected human can reduce the risk of future spread of COVID-19 To overcome those limitations, we conducted the current study to develop a stochastic SVITR mathematical model for the transmission dynamics of COVID-19 pandemic by introducing treated and vaccinated classes.
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