Nonlocal and nonsingular kernel-based fractional dynamics of infectious disease with waning immunity

Volume 38, Issue 1, pp 98--110 https://dx.doi.org/10.22436/jmcs.038.01.07

Publication Date: November 27, 2024 Submission Date: October 14, 2024 Revision Date: October 24, 2024 Accteptance Date: November 14, 2024

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Authors

R. Jan - Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia. - Mathematics Research Center, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey. S. Boulaaras - Department of Mathematics, College of Science, Qassim University, 51452, Buraydah, Saudi Arabia. I. A. Khan - Institute of Numerical Sciences, Kohat University of Science \(\&\) Technology, Kohat 26000, KPK, Pakistan. N. N. A. Razak - Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia.

Abstract

The burden of infections is a critical public health issue, and addressing it requires a multifaceted approach involving healthcare systems, governments, and communities. In this work, the dynamics of Japanese encephalitis (JE) is constructed with waning immunity using the Atangana-Baleanu fractional derivative. We introduce the fundamental theory related to the proposed fractional operator for the evaluation of the dynamics. The recommended model of the infection is examined for the essential results and the endemic indicator \(\mathcal{R}_0\) is determined with the help of next generation matrix approach. The existence and uniqueness of the solution of fractional-order system are evaluated via fixed point theory. Moreover, a newly developed numerical method is applied to iteratively solve our fractional-order model. Numerical simulations suggest that the management strategies are productive in reducing the prevalence of JE in humans, mosquitoes, and pigs. The fractional-order derivative provides more precise and realistic insights into the dynamics of JE, as evidenced by numerical findings that demonstrate the impact of various input factors on infection dynamics. Our research underscores the role of different factors of the recommended system for the management and control of the infection.

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Keywords

• Infectious disease
• fractional dynamics
• fixed-point theory
• existence of solution
• disease control
• public health

MSC

•  92D25
•  92D30

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