Abstract
In this paper, a novel coronavirus (COVID-19) model is proposed and investigated. In fact, the pandemic spread through a close contact between infected people and other people but sometimes the infected people could show two cases; the first is symptomatic and the other is asymptomatic (carrier) as the source of the risk. The outbreak of Covid-19 virus is described by a mathematical model dividing the population into four classes. The first class represents the susceptible people who are unaware of the disease. The second class refers to the susceptible people who are aware of the epidemic by media coverage. The third class is the carrier individuals (asymptomatic) and the fourth class represents the infected individuals. The existence, uniqueness and bounded-ness of the solutions of the model are discussed. All possible equilibrium points are determined. The locally asymptotically stable of the model is studied. Suitable Lyapunov functions are used to investigate the globally asymptotical stability of the model. Finally, numerical simulation is carried out to confirm the analytical results and to understand the effect of varying the parameters of how the disease spreads.
Highlights
In November 2002, the severe acute respiratory syndrome coronavirus emerged in China causing global anxiety as the outbreak rapidly spreads, and by July 2003, had resulted in over 8000 cases in 26 countries
The initial point for I(0) = 25, we assume that the C(0) = 10, susceptible individuals denoted by (Sa) = 10, susceptible individuals denoted by (Su) = 15 and v = 20. Using this initial point and simulated the system (1), we get the values of parameters shown in Table 1, whereas the basic reproduction number is estimated R0 = 0.914 < 1 with condition (8b), we obtain the dynamical behavior of system (3) converge to COVID-19 free equilibrium point E0 = (901096,0,0,0,0), illustrating its asymptotical stability that is stated in Theorem (2)
If the increase effect of the contact rate between Su and v (β), as well as used the values of parameters shown in Table 1 with d = 1, and β = 1.555 × 10−4., we obtain the dynamical behavior of system (3) still converge to COVID-19 equilibrium point E1 = ((61636,170389,25,334,0.25)), illustrating its asymptotical stability that is stated in Theorem (3)
Summary
In November 2002, the severe acute respiratory syndrome coronavirus emerged in China causing global anxiety as the outbreak rapidly spreads, and by July 2003, had resulted in over 8000 cases in 26 countries. Since December 2019, a novel corona virus, named (COVID-19), emerged in Wuhan, China and the epidemic has globally spread, updated on January 30, 2020, COVID-19 was declared a public health emergency of international concern. It caused more than 200,000 deaths out of 3,177,500 cases in the world among which 1,434,000 in Europe, 1,291,000 in Americas, 148,000 in Western Pacific and other cases in Asia and Africa [5]. The effect of media coverage to raise the people's awareness to the risk of the coronavirus and the effect of the direct contact with carrier individuals on breaking out the COVID-19 among people are shown by numerical simulation of the proposed model
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