Abstract
In this study, we use a compartmental nonlinear deterministic mathematical model to investigate the effect of different optimal control strategies in controlling Tuberculosis (TB) disease transmission in the community. We employ stability theory of differential equations to investigate the qualitative behavior of the model by obtaining the basic reproduction number and determining the local stability conditions for the disease-free and endemic equilibria. We consider three control strategies representing distancing, case finding, and treatment efforts and numerically compare the levels of exposed and infectious populations with and without control strategies. The results suggest that combination of all controls is the best strategy to eradicate TB disease from the community at an optimal level with minimum cost of interventions.
Highlights
TB is a chronic infection of the bacteria caused by Mycobacterium TB, which was discovered by Koch in 1882
6 Conclusion In this paper, we developed a dynamic model for TB transmission in the Haramaya district of Ethiopia based on active-TB incidence data recorded by the district health office and the Haramaya hospital
The basic reproduction number and local stability conditions of the equilibria were determined, and the basic reproduction number was used to perform the sensitivity analysis that identified the role of each parameter used in the model to the spread of TB disease
Summary
TB is a chronic infection of the bacteria caused by Mycobacterium TB, which was discovered by Koch in 1882. Gao and Huang [12] analyzed TB model that incorporates vaccination of susceptible individuals, identification for treatment of latently infected individuals, and treatment of individuals with active TB Their analysis showed that the combined implementation of three controls is most effective and less expensive among different strategies. Using the data of active-TB incidence obtained from 1970 to 2009, they estimated the parameters by the least-squares curve fitting They considered three control mechanisms (distancing, case finding, and case holding efforts) and used optimal control programs to minimize the number of exposed and infectious individuals and the cost of implementing the control treatment. 4, we formulate and analytically study an optimal control problem using Pontryagin’s maximum Based on this model flow diagram, the dynamics of the model is given by the following system of differential equations:.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
