## Jñānābha‎, Vol. 52 (2) (2022), (138-152)

MATHEMATICAL MODELLING AND SENSITIVITY ANALYSIS OF EFFECT OF GLOBAL WARMING ON CARRIER BASED INFECTIOUS DISEASES

By

Maninder Singh Arora1 , Shikha Singh2, Ashish Omar3 and S. N. Mishra4

1,2,3Department of Mathematics, PPN Postgraduate College, (CSJM University), Kanpur-208001, Uttar Pradesh, India

4Department of Mathematics, BND College, (CSJM University), Kanpur-208001, Uttar Pradesh, India

Email: maninderarora120@gmail.com, sshikha22976@yahoo.co.in, ashishomar999@gmail.com,snmishra2006@gmail.com

(Received : December 06, 2020; In format : December 13, 2020; Accepted : October 11, 2022)

DOI: https://doi.org/10.58250/jnanabha.2022.52216

Abstract

The effect of global warming on the proliferation of carrier dependent infectious diseases is exigent. In this paper, we have proposed and analysed a non-linear mathematical model to study the deleterious effect of rise in global temperature on the spread of carrier dependent infectious diseases due to increased carrier immigration. The model comprises five dependent variables, namely, the density of susceptible population, the density of infected population, the density of carrier population, the concentration of carbon dioxide and the global average temperature. Driven by existing literature and data, the global average temperature is assumed to be proportional to the increased level of CO2 . The natural as well as anthropogenic emissions that result in the upward climb of CO2  concentration in the atmosphere are considered in the model. The carrier population is assumed to grow logistically. The long-term behaviour of the model is estimated through the stability theory of differential equations. A basic differential sensitivity analysis is also conducted to assess the sensitivity of model solutions with respect to key parameters of the dynamical system. Numerical simulations are carried out to illustrate the analytical results.

2020 Mathematical Sciences Classification: 34D20, 34D23.

Keywords and Phrases: Carriers, Carbon Dioxide, Simulation, Stability, Sensitivity - analysis