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# A Nonstandard Computational Investigation of SEIR Model with Fuzzy Transmission, Recovery and Death Rates

Ahmed H. Msmali1, Fazal Dayan2,*, Muhammad Rafiq3, Nauman Ahmed4, Abdullah Ali H. Ahmadini1, Hassan A. Hamali5

1 Department of Mathematics, College of Science, Jazan University, Jazan, 45142, Saudi Arabia
2 Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan
3 Department of Mathematics, Faculty of Science & Technology, University of Central Punjab, Lahore, Pakistan
4 Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan
5 Department of Medical Laboratory Technology, Faculty of Applied Medical Sciences, Jazan University, P.O. Box 1906, Jazan, 45142, Saudi Arabia

* Corresponding Author: Fazal Dayan. Email:

Computers, Materials & Continua 2023, 77(2), 2251-2269. https://doi.org/10.32604/cmc.2023.040266

## Abstract

In this article, a Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is considered. The equilibrium analysis and reproduction number are studied. The conventional models have made assumptions of homogeneity in disease transmission that contradict the actual reality. However, it is crucial to consider the heterogeneity of the transmission rate when modeling disease dynamics. Describing the heterogeneity of disease transmission mathematically can be achieved by incorporating fuzzy theory. A numerical scheme nonstandard, finite difference (NSFD) approach is developed for the studied model and the results of numerical simulations are presented. Simulations of the constructed scheme are presented. The positivity, convergence and consistency of the developed technique are investigated using mathematical induction, Jacobean matrix and Taylor series expansions respectively. The suggested scheme preserves all these essential characteristics of the disease dynamical models. The numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease. Moreover, the obtained method generates plausible predictions that can be used by regulators to support the decision-making process to design and develop control strategies. Effects of the natural immunity on the infected class are studied which reveals that an increase in natural immunity can decrease the infection and vice versa.

## Keywords

A. H. Msmali, F. Dayan, M. Rafiq, N. Ahmed, A. A. H. Ahmadini et al., "A nonstandard computational investigation of seir model with fuzzy transmission, recovery and death rates," Computers, Materials & Continua, vol. 77, no.2, pp. 2251–2269, 2023.

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