Abstract
In this study, the spreading of the pandemic coronavirus disease (COVID-19) is formulated mathematically. The objective of this study is to stop or slow the spread of COVID-19. In fact, to stop the spread of COVID-19, the vaccine of the disease is needed. However, in the absence of the vaccine, people must have to obey curfew and social distancing and follow the media alert coverage rule. In order to maintain these alternative factors, we must obey the modeling rule. Therefore, the impact of curfew, media alert coverage, and social distance between the individuals on the outbreak of disease is considered. Five ordinary differential equations of the first-order are used to represent the model. The solution properties of the system are discussed. The equilibria and the basic reproduction number are computed. The local and global stabilities are studied. The occurrence of local bifurcation near the disease-free equilibrium point is investigated. Numerical simulation is carried out in applying the model to the sample of the Iraqi population through solving the model using the Runge–Kutta fourth-order method with the help of Matlab. It is observed that the complete application of the curfew and social distance makes the basic reproduction number less than one and hence prevents the outbreak of disease. However, increasing the media alert coverage does not prevent the outbreak of disease completely, instead of that it reduces the spread, which means the disease is under control, by reducing the basic reproduction number and making it an approachable one.
Highlights
Musa et al [9] employed an SEIR model to study the transmission dynamics of SARS-CoV-2 outbreaks in Nigeria; the model incorporates a different group of populations, namely, high and moderate risk populations. ey used the model to investigate the influence of each population on the overall transmission dynamics
An epidemic model to describe the spread of COVID-19 is proposed using the first-order ordinary differential equations. e model takes into account the impact of the curfew and media coverage on the control of the spreading of disease
It is observed that model (1) has two equilibrium points: the disease-free point that is stable, which means the disease is under control from a biological point of view, when the basic reproduction number satisfies R0 < 1 and unstable for R0 > 1, and the endemic equilibrium point that is stable, which means the disease out of control from a biological point of view, whenever the disease-free becomes unstable
Summary
The dynamics of COVID-19 are mathematically modeled using first-order ordinary differential equations. Erefore, the population can be divided into five main compartments; these are the susceptible individuals at time t denoted by S(t) in which the individuals are at risk of infection with COVID-19. E exposed individuals at time t are denoted by E(t), in which the individuals have contracted the COVID-19 but are not yet infectious. E infected individuals at time t are represented as I(t) in which the individuals are capable of spreading the disease, and they are having mild symptoms or not. E hospitalized infected individuals at time t are denoted by Ih(t), in which the individuals have severe symptoms or quarantined due to getting mild symptoms, and they put in the hospital to get treatment. The term (b2I/m + I) refers to the reduced value of the contact (transmission) rate in the case of reporting of the infectious individuals.
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