Authors
Isa Abdullahi Baba, Rabiu Aliyu Abdulkadir, Parvaneh Esmaili
Publication date
2020/2/15
Journal
Physica A: Statistical Mechanics and its Applications
Volume
540
Pages
123237
Publisher
North-Holland
Description
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 R 0. We also prove that when R 0≤ 1, the DFE is globally asymptotically stable and the disease dies out. When R 0> 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 u 1 (t) and u 2 (t), are also shown numerically.
Total citations
202020212022202320245117176
Scholar articles
IA Baba, RA Abdulkadir, P Esmaili - Physica A: Statistical Mechanics and its Applications, 2020