Analytical solutions of the transmissibility of the SARS-CoV-2 in three interactive populations

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