Analysis of tuberculosis model with saturated incidence rate and optimal control

Isa Abdullahi Baba, Rabiu Aliyu Abdulkadir and Parvaneh Esmaili

Physica A: Statistical Mechanics and its Applications, 2020, vol. 540, issue C

Abstract: We study a basic tuberculosis model using saturated incidence rate. Incorporated in the model is the therapeutic treatments given to infected individuals. Global stability of both the disease-free equilibrium and the endemic equilibrium are determined by a threshold quantity, the basic reproduction ratio R0. We also prove that when R0≤1, the DFE is globally asymptotically stable and the disease dies out. When R0>1, the unique endemic equilibrium exists, is globally asymptotically stable, and epidemic occurs. Optimal control is applied to the model, to show how the use of optimal control strategy will reduce the number of infectious individuals. The result is supported by numerical computations. The significance of δ (the parameter that measures the psychological or inhibitory effect), and the optimal control functions u1(t) and u2(t), are also shown numerically.

Keywords: Saturated incidence rate; Tuberculosis model; SEIR model; Basic reproduction ratio; Global stability; Optimal control; Numerical computation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119318175

DOI: 10.1016/j.physa.2019.123237

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