Global Dynamics of a Social Hierarchy-Stratified Malaria Model: Insight from Fractional Calculus

Sulaimon F. Abimbade, Furaha M. Chuma, Sunday O. Sangoniyi, Ramoshweu S. Lebelo, Kazeem O. Okosun and Samson Olaniyi ()
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Sulaimon F. Abimbade: Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso 212102, Nigeria
Furaha M. Chuma: Department of Physics, Mathematics and Informatics, Dar es Salaam University College of Education, Dar es Salaam 2329, Tanzania
Sunday O. Sangoniyi: Department of Mathematics and Computing Science Education, Emmanuel Alayande University of Education, Oyo 211172, Nigeria
Ramoshweu S. Lebelo: Department of Education, Vaal University of Technology, Vanderbijilpark 1911, South Africa
Kazeem O. Okosun: Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA
Samson Olaniyi: Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso 212102, Nigeria

Mathematics, 2024, vol. 12, issue 10, 1-19

Abstract: In this study, a mathematical model for the transmission dynamics of malaria among different socioeconomic groups in the human population interacting with a susceptible-infectious vector population is presented and analysed using a fractional-order derivative of the Caputo type. The total human population is stratified into two distinguished classes of lower and higher income individuals, with each class further subdivided into susceptible, infectious, and recovered populations. The socio hierachy-structured fractional-order malaria model is analyzed through the application of different dynamical system tools. The theory of positivity and boundedness based on the generalized mean value theorem is employed to investigate the basic properties of solutions of the model, while the Banach fixed point theory approach is used to prove the existence and uniqueness of the solution. Furthermore, unlike the existing related studies, comprehensive global asymptotic dynamics of the fractional-order malaria model around both disease-free and endemic equilibria are explored by generalizing the usual classical methods for establishing global asymptotic stability of the steady states. The asymptotic behavior of the trajectories of the system are graphically illustrated at different values of the fractional (noninteger) order.

Keywords: fractional-order system; social hierarchy model; malaria dynamics; Banach fixed point theory; global stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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