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Open Access

ARTICLE

A Dynamical Study of Modeling the Transmission of Typhoid Fever through Delayed Strategies

Muhammad Tashfeen1, Fazal Dayan1, Muhammad Aziz Ur Rehman1, Thabet Abdeljawad2,3,4,5,*, Aiman Mukheimer2
1 Department of Mathematics, School of Science, University of Management and Technology, Lahore, 54000, Pakistan
2 Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia
3 Department of Medical Research, China Medical University, Taichung, 40402, Taiwan
4 Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako, Makgatho Health Sciences University, Ga-Rankuwa, 0208, South Africa
5 Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Hawally, 32093, Kuwait
* Corresponding Author: Thabet Abdeljawad. Email: email
(This article belongs to the Special Issue: Mathematical Aspects of Computational Biology and Bioinformatics-II)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2024.053242

Received 28 April 2024; Accepted 28 July 2024; Published online 27 August 2024

Abstract

This study analyzes the transmission of typhoid fever caused by Salmonella typhi using a mathematical model that highlights the significance of delay in its effectiveness. Time delays can affect the nature of patterns and slow down the emergence of patterns in infected population density. The analyzed model is expanded with the equilibrium analysis, reproduction number, and stability analysis. This study aims to establish and explore the non-standard finite difference (NSFD) scheme for the typhoid fever virus transmission model with a time delay. In addition, the forward Euler method and Runge-Kutta method of order 4 (RK-4) are also applied in the present research. Some significant properties, such as convergence, positivity, boundedness, and consistency, are explored, and the proposed scheme preserves all the mentioned properties. The theoretical validation is conducted on how NSFD outperforms other methods in emulating key aspects of the continuous model, such as positive solution, stability, and equilibrium about delay. Hence, the above analysis also shows some of the limitations of the conventional finite difference methods, such as forward Euler and RK-4 in simulating such critical behaviors. This becomes more apparent when using larger steps. This indicated that NSFD is beneficial in identifying the essential characteristics of the continuous model with higher accuracy than the traditional approaches.

Keywords

Typhoid virus; delay epidemic model; stability; consistency; global stability

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