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Mathematical modelling and optimal control strategies of the transmission of enterovirus

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Title: Mathematical modelling and optimal control strategies of the transmission of enterovirus
Authors: Mabotsa, Malebese
Contributors: Munganga, J. M. W., Hassan, Adamu Shitu
Publication Year: 2022
Collection: University of South Africa: UNISA Institutional Repository
Subject Terms: Mathematical modelling, Enterovirus, Basic reproduction number, Next generation matrix method, Lyapunov functions, Volterra-Lyapunov matrices, Optimal control, Pontrayagin's Maximum principle, 616.9180015118, Enterovirus diseases -- Transmission -- Mathematical models, Matrix analytic methods, Maximum principles (Mathematics)
Description: We propose a mathematical model for the transmission dynamics of enterovirus. We prove that if the basic reproduction number R0 1, a suitable Lyapunov function is used to establish the global stability of the disease free equilibrium, in which case the infection will die out over time. Our analysis further establish the global stability of the endemic equilibrium based on the approach of Volterra-Lyapunov matrices if R0 > 1. Our ndings show that when R0 > 1, the endemic equilibrium is globally asymptotically stable. In this case, the enterovirus will invade the population. It is shown that by reducing direct transmission rate by 80%, the basic reproduction number can be reduced below one and thus controlling the infection. Using optimal control with hygiene and sanitation campaigns as control measures, it is shown that the disease can be controlled within a shorter period of time as compared to minimizing the direct contact rate by 80%. Numerical simulations are provided to illustrate the results. ; M. Sc. (Applied Mathematics) ; Mathematical Sciences
Document Type: doctoral or postdoctoral thesis
File Description: 1 online resource (60 leaves) : black and white illustration, color graphs; application/pdf
Language: English
Relation: https://hdl.handle.net/10500/28986
Availability: https://hdl.handle.net/10500/28986
Accession Number: edsbas.4465FECB
Database: BASE
Description
Abstract:We propose a mathematical model for the transmission dynamics of enterovirus. We prove that if the basic reproduction number R0 1, a suitable Lyapunov function is used to establish the global stability of the disease free equilibrium, in which case the infection will die out over time. Our analysis further establish the global stability of the endemic equilibrium based on the approach of Volterra-Lyapunov matrices if R0 > 1. Our ndings show that when R0 > 1, the endemic equilibrium is globally asymptotically stable. In this case, the enterovirus will invade the population. It is shown that by reducing direct transmission rate by 80%, the basic reproduction number can be reduced below one and thus controlling the infection. Using optimal control with hygiene and sanitation campaigns as control measures, it is shown that the disease can be controlled within a shorter period of time as compared to minimizing the direct contact rate by 80%. Numerical simulations are provided to illustrate the results. ; M. Sc. (Applied Mathematics) ; Mathematical Sciences