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Journal of Applied Nonlinear Dynamics 13(3) (2024) 491--505 | DOI:10.5890/JAND.2024.09.006

Sumit Kumar$^1$, Sandeep Sharma$^2$, Atul Kashyap$^3$, Nitu Kumari$^1$

$^1$ School of Mathematical & Statistical Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, 175005, India

$^2$ Department of Mathematics, DIT University, Dehradun, Uttarakhand, 248009, India

$^3$ BBMK University, Dhanbad, 826001 Jharkhand, India

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Abstract

In 2015, south and north American countries witnessed an epidemic of Zika fever caused by the Zika virus (ZIKV). The virus got transmitted to humans primarily by the bite of aedes mosquitoes. Brazil and Colombia were among the countries which suffered the most during this Zika pandemic that lasted for almost three years. This paper introduces a non-linear extended SIR model to model the Zika pandemic, where two separate populations, humans and mosquitoes, are considered. Official data provided by health agencies drag our attention toward a possible relationship between environmental pollution and Zika infections. To model the effect of pollution, we have incorporated a stressed compartment of the human population that consists of those exposed to environmental pollution. We have derived the expression and actual value of Colombia's basic reproduction number of the Zika outbreak. Also, we have derived the conditions under which the disease-free and endemic equilibrium points of the model become stable and unstable, respectively. We have also shown whether the model will show backward bifurcation or not. A detailed qualitative analysis of the model has been done. We have conducted comprehensive numerical simulations to support our theoretical findings. Lastly, we investigated a massive Zika virus outbreak in Colombia (2015-17) with the help of the proposed model. The impact of environmental pollution has also been studied in the present study. Our work is the first official data-driven establishment between ecological contamination and the spread of the Zika outbreak.

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