Title: Global stability and optimal control of melioidosis transmission model with hygiene care and treatment in human and animal populations

Authors: Ratchada Viriyapong; Sunisa Tavaen

Addresses: Faculty of Science, Department of Mathematics, Naresuan University, Phitsanulok, 65000, Thailand ' Faculty of Science, Department of Mathematics, Naresuan University, Phitsanulok, 65000, Thailand

Abstract: A compartmental deterministic mathematical model for melioidosis transmission is proposed. It involves human and animal population and bacteria. We present two main equilibrium points (disease-free and endemic) with the analysis of their local stability. The basic reproduction number and its sensitivity index to the parameters in the model are calculated. Lyapunov's direct method is used to analyse the global stability of endemic equilibrium point. Further, by using Pontryagin's minimum principle, the optimal control problem is constructed with two controls, i.e., hygiene care and treatment controls for human population. Finally, the numerical simulations are established and our results show that a combination of both controls give more impact in reducing the number of infected human and bacteria than in reducing the number of infected animals. Because melioidosis prevalence is still increasing, more effort in sharing knowledge and controlling the spreading of this disease is still much required.

Keywords: melioidosis; hygiene care; numerical study; optimal control; treatment; Lyapunov's direct method; Pontryagin's minimum principle.

DOI: 10.1504/IJMIC.2020.112294

International Journal of Modelling, Identification and Control, 2020 Vol.34 No.4, pp.301 - 315

Received: 20 Aug 2019
Accepted: 25 Mar 2020
Published online: 07 Jan 2021 *

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