Abstract
This paper resolves analytically a mathematical model that reproduces the transmission of Covid-19 in three interactive populations, i.e. from the initial source of contagion associated with the bat population, subsequently transmitted to unknown host (usually associate with pangolins). The host were sent and distributed to Seafood Market in Wuhan (defined reservoir), and finally infected to the human population. The model is based on a system of ten differential equations reproducing all the possible infection scenarios among all of them, that is: (1) there is no infection in any of the three populations, (2) only the population of bats is infected, (3) only the pangolins, (4) only the human people. Later, combinations between them, this is: (5) both the bat and pangolin populations, (6) bats and humans, (7) pangolins and humans, and finally, (8) all the previous populations. In each scenario, I deduced the critical points as well as the eigenvalues that indicate the equilibrium conditions. Finally, it is demonstrated the validity of the model with the data corresponding to the second wave of infections in Australia.
Highlights
The World Health Organization declared a new pandemic caused by a virus called as Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) on March 11, 2020, after the first case detected in the Seafood Market of Wuhan province in China in December 2019
This model is based on the transmission of the virus between three different populations, it means, from the source of contagion in humans originated in bats [7], later transmitted to an unknown host
The model is based on a compartmental scheme of the SIR-type (Susceptible-Infected-Recovered), and despite the simplicity of the model, eight critical points are obtained representing the different infection scenarios among the three populations considered in this paper
Summary
The World Health Organization declared a new pandemic caused by a virus called as Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) on March 11, 2020, after the first case detected in the Seafood Market of Wuhan province in China in December 2019. Up-to-date, there is a wide range of mathematical models that explain the spread of the virus, but most of all are based on contagion in the human population [1,2,3,4,5]. This paper only determined an only equilibrium condition corresponding to the trivial solution of the system. This model is based on the transmission of the virus between three different populations, it means, from the source of contagion in humans originated in bats [7], later transmitted to an unknown host. As indicated Chen et al, the host were hunted and distributed in the Seafood Marked in Wuhan (defined as Reservoir), and infected to the human population
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