Impact of pangolin bootleg market on the dynamics of COVID-19 model

Abd Ullah; Saeed Ahmad; Ghaus Ur Rahman; M M Alqarni; Emad E Mahmoud

doi:10.1016/j.rinp.2021.103913

Impact of pangolin bootleg market on the dynamics of COVID-19 model

Results Phys. 2021 Apr:23:103913. doi: 10.1016/j.rinp.2021.103913. Epub 2021 Feb 19.

Authors

Abd Ullah¹, Saeed Ahmad¹, Ghaus Ur Rahman², M M Alqarni³, Emad E Mahmoud^{4

5}

Affiliations

¹ Department of Mathematics, University of Malakand Chakdara, Dir (L), Pakhtunkhwa, Pakistan.
² Department of Mathematics and Statistics, University of Swat, District Swat, Pakistan.
³ Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia.
⁴ Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.
⁵ Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.

Abstract

In this paper we consider ant-eating pangolin as a possible source of the novel corona virus (COVID-19) and propose a new mathematical model describing the dynamics of COVID-19 pandemic. Our new model is based on the hypotheses that the pangolin and human populations are divided into measurable partitions and also incorporates pangolin bootleg market or reservoir. First we study the important mathematical properties like existence, boundedness and positivity of solution of the proposed model. After finding the threshold quantity for the underlying model, the possible stationary states are explored. We exploit linearization as well as Lyapanuv function theory to exhibit local stability analysis of the model in terms of the threshold quantity. We then discuss the global stability analyses of the newly introduced model and found conditions for its stability in terms of the basic reproduction number. It is also shown that for certain values of $R_{0}$ , our model exhibits a backward bifurcation. Numerical simulations are performed to verify and support our analytical findings.

Keywords: COVID-19; Life span; Pangolin bootleg market; Peddle rate; Stability; Wastage rate.