A biological mathematical model of vector-host disease with saturated treatment function and optimal control strategies

1.
Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
2.
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
3.
Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, Pakistan
4.
Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia
5.
Department of Mathematics, Faculty of Science King Abdulaziz University, P. O. Box 80203 Jeddah 21589, Saudi Arabia

Received: 12 March 2020 Accepted: 14 May 2020 Published: 01 June 2020
MSC : 92D25, 49J15, 93D20

Abstract
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The aims of this paper to explore the dynamics of the vector-host disease with saturated treatment function. Initially, we formulate the model by considering three different classes for human and two for the vector population. The use of the treatment function in the model and their brief analysis for the case of disease-free and endemic case are briefly shown. We show that the basic reproduction number (<or >) than unity, the disease-free and endemic cases are stable locally and globally. Further, we apply the optimal control technique by choosing four control variables in order to maximize the population of susceptible and recovered human and to minimize the population of infected humans and vector. We discuss the results in details of the optimal controls model and show their existence. Furthermore, we solve the optimality system numerically in connection with the system of no control and the optimal control characterization together with adjoint system, and consider a set of different controls to simulate the models. The considerable best possible strategy that can best minimize the infection in human infected individuals is the use of all controls simultaneously. Finally, we conclude that the work with effective control strategies.
- optimal control applications,
- vector-host model,
- saturated treatment,
- basic reproduction number,
- global stability,
- numerical simulations
Citation: Muhammad Altaf Khan, Navid Iqbal, Yasir Khan, Ebraheem Alzahrani. A biological mathematical model of vector-host disease with saturated treatment function and optimal control strategies[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3972-3997. doi: 10.3934/mbe.2020220

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Abstract

The aims of this paper to explore the dynamics of the vector-host disease with saturated treatment function. Initially, we formulate the model by considering three different classes for human and two for the vector population. The use of the treatment function in the model and their brief analysis for the case of disease-free and endemic case are briefly shown. We show that the basic reproduction number (<or >) than unity, the disease-free and endemic cases are stable locally and globally. Further, we apply the optimal control technique by choosing four control variables in order to maximize the population of susceptible and recovered human and to minimize the population of infected humans and vector. We discuss the results in details of the optimal controls model and show their existence. Furthermore, we solve the optimality system numerically in connection with the system of no control and the optimal control characterization together with adjoint system, and consider a set of different controls to simulate the models. The considerable best possible strategy that can best minimize the infection in human infected individuals is the use of all controls simultaneously. Finally, we conclude that the work with effective control strategies.

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