The role of vaccination in curbing tuberculosis epidemic
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Date
2019-09-13
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Modeling Earth Systems and Environment
Abstract
This work studies the impact of vaccine in controlling tuberculosis (TB) epidemic using susceptible, vaccinated, exposed, infectious and recovered compartmental model. This is necessitated due to the acclaimed ineffectiveness of BCG vaccine in combatting TB. The model is formulated using a non-linear system of ordinary differential equation which is normalised to eliminate the natural death factor (mu) so as to focus on other factors. The disease-free equilibrium and endemic equilibrium point (EEP) of the system are established alongside their local and global stabilities. Although the local stability of the EEP could not be established analytically due to the cumbersomeness of the EEP obtained, it is, however, established numerically. It is shown with the aid of numerical simulation carried out on the model that vaccination helps in reducing the tuberculosis epidemic and in fact, if the rates of contact and infectivity are reduced, further reduction in the rate of incidence (lambda) can be achieved. Further more, the reason why there is the need for a better vaccine to replace BCG vis-á-vis provision of better immunity coverage (theta → 0 and sigma → 0) and also, the need for the development of drugs that confer permanent or long lasting immunity (delta_2 → 0) is as well established. More vaccination proportion gives better outcome (tau → 1) and the introduced controls show their relevance in reducing the infection. The novelty of this research is the provision of guiding frame work for the pharmacists on the intrinsic features expected of any proposed vaccine to replace BCG while the expected recommendations from the doctors are established using optimal control.
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Keywords
Tuberculosis model, vaccination, optimal control, basic reproduction number, global stability, reinfection rate