Modeling the impact of early therapy for latent tuberculosis patients and its optimal control analysis
Journal of Biological Physics
Department of Mathematics, University of Zimbabwe, PO Box MP 167, Harare, Zimbabwe
Effective tuberculosis (TB) control depends on case findings to discover infectious cases, investigation of contacts of those with TB, as well as appropriate treatment. Adherence and successful completion of the treatment are equally important. Unfortunately, due to a number of personal, psychosocial, economic, medical, and health service factors, a significant number of TB patients become irregular and default from treatment. In this paper, a mathematical model is developed to assess the impact of early therapy for latent TB and non-adherence on controlling TB transmission dynamics. Equilibrium states of the model are determined and their local stability is examined. With the aid of the center manifold theory, it is established that the model undergoes a backward bifurcation. Qualitative mathematical analysis of the model suggests that a high level of latent tuberculosis case findings, coupled with a decrease of defaulting rate, may be effective in controlling TB transmission dynamics in the community. Population-level effects of organized campaigns to improve early therapy and to guarantee successful completion of each treatment are evaluated through numerical simulations and presented in support of the analytical results. © 2013 Springer Science+Business Media Dordrecht.
article; bacterial transmission; case finding; dynamics; early childhood intervention; health program; health promotion; latent tuberculosis; mathematical analysis; mathematical model; population research; priority journal; qualitative analysis; simulation; theory; tuberculosis control; Asymptomatic Diseases; Communicable Disease Control; Endemic Diseases; Humans; Latent Tuberculosis; Models, Statistical; Patient Compliance; Time Factors