Analysis of tuberculosis model with saturated incidence rate and optimal control

Baba, Isa Abdullahi; Abdulkadir, Rabiu Aliyu; Esmaılı, Parvaneh

doi:10.1016/j.physa.2019.123237

Cited by 36 publications

(19 citation statements)

References 12 publications

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“…A successful control should eradicate the infection from the population while simultaneously minimizing the control cost. The optimal control technique that has been used in many studies [3,11,16,19,20,43] can be utilized to achieve this aim. In this section, we apply control theory to determine the best strategy that will minimize the number of infected individuals while keeping the vaccination cost at a minimum.…”

Section: Optimal Control Problemmentioning

confidence: 99%

Stability analysis and optimal control of production-limiting disease in farm with two vaccines

Liu¹,

Lo²

2022

DCDS-B

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The transmission of production-limiting disease in farm, such as Neosporosis and Johne's disease, has brought a huge loss worldwide due to reproductive failure. This paper aims to provide a modeling framework for controlling the disease and investigating the spread dynamics of Neospora caninum-infected dairy as a case study. In particular, a dynamic model for production-limiting disease transmission in the farm is proposed. It incorporates the vertical and horizontal transmission routes and two vaccines. The threshold parameter, basic reproduction number R 0 , is derived and qualitatively used to explore the stability of the equilibria. Global stability of the disease-free and endemic equilibria is investigated using the comparison theorem or geometric approach. On the case study of Neospora caninum-infected dairy in Switzerland, sensitivity analysis of all involved parameters with respect to the basic reproduction number R 0 has been performed. Through Pontryagin's maximum principle, the optimal control problem is discussed to determine the optimal vaccination coverage rate while minimizing the number of infected individuals and control cost at the same time. Moreover, numerical simulations are performed to support the analytical findings. The present study provides useful information on the understanding of production-limiting disease prevention on a farm.

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Section: Optimal Control Problemmentioning

confidence: 99%

Stability analysis and optimal control of production-limiting disease in farm with two vaccines

Liu¹,

Lo²

2022

DCDS-B

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“…In consequence, we are led to design the feedback map G ϕ (•) of Eq. (14). For that purpose we need first to compute the contingent cone T D ϕ (•).…”

Section: Theorem 1 Any Continuous Selection Of the Map G ϕ Provides Amentioning

confidence: 99%

“…Optimal control through either vaccination or isolation is investigated by application of Pontryagin's Maximum Principle. Using a basic SEI model with saturated incidence rate, Baba et al [14] studied the effect of optimal controller and awareness on the dynamic of Tuberculosis. In these works and in many others (see [15][16][17][18][19][20] and the references therein) the authors have solved the formulated control problems using classical results of control theory, in particular the famous Pontryagin's minimum principle [21].…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

A novel control set-valued approach with application to epidemic models

Boujallal

Elhia

Balatif

2020

J. Appl. Math. Comput.

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This work is considered in the framework of studies dedicated to the control problems, especially in epidemiology where the scientist are concerned to develop effective control strategies to minimize the number of infected individuals. In this paper, we set this problem as an asymptotic target control problem under mixed state-control constraints, for a general class of ordinary differential equations that model the temporal evolution of disease spread. The set of initial data, from which the number of infected people decrease to zero, is generated by a new type of Lyapunov functions defined in the sense of viability theory. The associated controls are provided via selections of adequately designed feedback map. The existence of such selections is improved by using Micheal selection theorem. Finally, an application to the SIRS epidemic model, with numerical simulations, is given to show the efficiency of our approach. To the best of our knowledge, our work is the first one that used a set-valued approach based on the viability theory to deal with an epidemic control problem.

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“…Then the optimal control strategy is applied for controlling the transmission of TB in child and adult populations. Using a basic SEI model with saturated incidence rate, Baba et al [34] studied the effect of optimal controller and awareness. It is noted that a considerable number of studies that deal with TB modelling use the basic SEI or SEIR model with only a single compartment of infectious people (see [35][36][37][38][39][40][41]).…”

Section: Introductionmentioning

confidence: 99%

Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays

Elhia¹,

Balatif

Boujallal³

et al. 2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this paper, we formulate an optimal control problem based on a tuberculosis model with multiple infectious compartments and time delays. In order to have a more realistic model that allows highlighting the role of detection, loss to follow-up and treatment in TB transmission, we propose an extension of the classical SEIR model by dividing infectious patients in the compartment (I) into three categories: undiagnosed infected (I), diagnosed patients who are under treatment (T) and diagnosed patients who are lost to follow-up (L). We incorporate in our model delays representing the incubation period and the time needed for treatment. We also introduce three control variables in our delayed system which represent prevention, detection and the efforts that prevent the failure of treatment. The purpose of our control strategies is to minimize the number of infected individuals and the cost of intervention. The existence of the optimal controls is investigated, and a characterization of the three controls is given using the Pontryagin's maximum principle with delays. To solve numerically the optimality system with delays, we present an adapted iterative method based on the iterative Forward-Backward Sweep Method (FBSM). Numerical simulations performed using Matlab are also provided. They indicate that the prevention control is the most effective one. To the best of our knowledge, it is the first work to apply optimal control theory to a TB model which considers infectious patients diagnosis, loss to follow-up phenomenon and multiple time delays.

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Analysis of tuberculosis model with saturated incidence rate and optimal control

Cited by 36 publications

References 12 publications

Stability analysis and optimal control of production-limiting disease in farm with two vaccines

Stability analysis and optimal control of production-limiting disease in farm with two vaccines

A novel control set-valued approach with application to epidemic models

Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays

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