Modelling the Optimal Control of Transmission Dynamics of Mycobacterium ulceran Infection

Autor:	Magreth Anga Kimaro, Daniel Oluwole Makinde, Estomih S. Massawe
Rok vydání:	2015
Předmět:	Equilibrium point education.field_of_study business.industry Population Optimal control Stability (probability) Nonlinear system Maximum principle Stability theory Medicine Applied mathematics business education Basic reproduction number
Zdroj:	Open Journal of Epidemiology. :229-243
ISSN:	2165-7467 2165-7459
DOI:	10.4236/ojepi.2015.54027
Popis:	This paper examines optimal control of transmission dynamics of Mycobacterium ulceran (MU) infection. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations, optimal control and computer simulation. The basic reproduction number of the reduced model system is obtained by using the next generation operator method. It is found that by using Ruth Hurwitz criteria, the disease free equilibrium point is locally asymptotically stable and using centre manifold theory, the model shows the transcritical (forward) bifurcation. Optimal control is applied to the model seeking to minimize the transmission dynamics of MU infection on human and water-bugs. Pontryagin’s maximum principle is used to characterize the optimal levels of the controls. The results of optimality are solved numerically using MATLAB software and the results show that optimal combination of two controls (environmental and health education for prevention) and (water and environmental purification) minimizes the MU infection in the population.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e2147e71321e163bdf672251a1a35f24 https://doi.org/10.4236/ojepi.2015.54027 Zobrazit plný text záznamu