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In this paper, we have formulated a mathematical model based on a series of ordinary dierential equations to study the transmission dynamics of infectious diseases that exhibit relapse. The basic reproduction number of the model was computed using the next generation matrix method. The existence of the equilibrium points of the model was investigated and stability analysis carried out. The disease free equilibrium point was found to be locally asymptotically stable when R0 < 1 and unstable when R0 > 1 and globally asymptotically stable when R0 < 1 and unstable when R0 > 1. The endemic equilibrium point was found to be locally and globally asymptotically stable when R0 > 1. The center manifold theory was used to investigate the type of bifurcation at R0 = 1.
Huo HF, Qiu GM. Stability of a mathematical model of malaria transmission with relapse.
Abstract and Applied Analysis. 2014;2014. Article ID 289349 Kermack WO, McKendrick AG. Contributions to the mathematical theory of epidemics, part
I. Proceedings of the Royal Society of London Series A. vol. 1927;115:700-721. Kaplan E, Margaret L. Modelling of AIDS and the AIDS epidemic. New York: Raven; 1994.
Dobson JR, Grenfell BT AP. Epidemic dynamics at the human-animal interface. Science. ;326 1362-1367.
Tudor D. A deterministic model for herpes infections in human and animal populations. SIAM Review. 1990;32(1):136-139.
Vargas-De-Leon C. On the global stability of infectious diseases models with relapse.
Abstraction & Application. 2013;9:50-61.
Chen Y, Li J, Zou S. Global dynamics of an epidemic model with relapse and nonlinear incidence. Math Meth Appl Sci. 2018;19.
Ghosh M, Olaniyi S, Obabiyi OS. Mathematical analysis of reinfection and relapse in malaria dynamics. Applied Mathematics and Computation. 2020;373:125044.
Diekmann O, Heesterbeek JAP, Metz JAJ. On the denition and the computation of the basic reproduction ratio R0 in models of infectious diseases and heterogenous populations. J. Math.
Van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences. ;180(1-2):29-48.
Garba SM, Gumel AB, Bakar MRA. Backward bifurcations in dengue transmission dynamics. Mathematical Biosciences. 2008;15(1):11-25.
Chitnis N, Cushing JM, Hyman JM. Bifurcation analysis of a mathematical model for malaria transmission. SIAM J. APPL. MATH. 2006;67(1): 24-45.
Piazza N, Hao W. Bifurcation and sensitivity analysis of immunity duration in a Epidemic.
International Journal of Numerical Analysis and Modelling, Series B. 2013;4(2):179-202.
Arion J, Mccluskey CC, Van Den Driessche P. Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM. J. APPL. MATH. 2003;64(1):260-276.
Huang W, Cooke KL, Carlos C. Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM. J. APPL. MATH. 1992;52(3):835-854.
Castillo Chavez C, Song B. Dynamical models of tuberculosis and their applications. Mathematical Biosciences and Engineering. 2004;1(2):361-404.
Enagi AI, Ibrahim MO, Akinwande NI, et al. A mathematical model of tuberculosis control incorporating vaccination, latency and infectious treatments (Case Study of Nigeria).
International Journal of Mathematics and Computer Science. 2017;12(2):97106. LaSalle JP. The stability of dynamical systems. Regional Conference Series in Applied
Mathematics. SIAM, Philadelphia, PA; 1976.