Open Access Open Access  Restricted Access Subscription or Fee Access

Dynamical behavior of a tuberculosis model with outcome of reinfection and optimal steering

T. K. Kar, Prasanta Kumar Mondal

Abstract


In this paper, we propose and analyze a tuberculosis (TB) model and assume that treated individual may be again infected by infectious individual. The basic reproduction number is derived and it is observed that model exhibits two bifurcations viz. transcritical bifurcation when the basic reproductive number and backward bifurcation which occurs due to sufficient level of reinfection. We extend our deterministic model to a stochastic version and study the dynamical behaviors of the deterministic model system in stochastic environment. We mainly use the Lyapunov functional to establish the global stability of endemic equilibrium point in stochastic sense. The effect of intensity of white noise on stability of the system is investigated using Euler’s method. We also apply optimal control theory to control the disease using vaccination and treatment as control variable. The objective function is to minimize the exposed and infectious individuals as well as the cost associated with it. Lastly, some simulations are given to verify our analytical results.

Keywords


Tuberculosis, reproduction number, transcritical bifurcation, backward bifurcation, optimal control.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.