Browsing by Author "Othman, Wan Ainun Mior"

Now showing 1 - 3 of 3
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    A compartmental model on the effect of quarantine on MDR-TB
    (International Journal of Mathematics and Computer Science, 2019) Ayinla, Ally Yeketi; Othman, Wan Ainun Mior
    This paper presents a five compartmental deterministic model to study the effect of quarantine in managing multidrug-resistant tuberculosis (MDR-TB). We established that the model exhibits two equilibria; disease free equilibrium (DFE) and endemic equilibrium point (EEP). The DFE was shown to be locally asymptotically stable when the basic reproduction number, R_0 is less than unity (R_0< 1). The global stability of both the DFE and EEP were established with the aid of constructed Lyapunov functions. We proved that the model undergoes backward bifurcation, which gives direction to the medical experts that keeping the basic reproduction number less than unity (R_0< 1) is not enough to curtail the spread of the infection but rather think of other measures. The numerical simulation done gives a pictorial representation of the impact of quarantine in managing MDR-TB as it helps in reducing the disease incidence.
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    A Mathematical Model of the Tuberculosis Epidemic
    (Acta Biotheoretica, 2021-04-19) Ayinla, Ally Yeketi; Othman, Wan Ainun Mior; Rabiu, Musa
    Tuberculosis has continued to retain its title as “the captain among these men of death”. This is evident as it is the leading cause of death globally from a single infectious agent. TB as it is fondly called has become a major threat to the achievement of the sustainable development goals (SDG) and hence require inputs from different research disciplines. This work presents a mathematical model of tuberculosis. A compartmental model of seven classes was used in the model formulation comprising of the susceptible S, vaccinated V, exposed E, undiagnosed infectious I_1, diagnosed infectious I_2, treated T and recovered R. The stability analysis of the model was established as well as the condition for the model to undergo backward bifurcation. With the existence of backward bifurcation, keeping the basic reproduction number less than unity (R_0< 1) is no more sufficient to keep TB out of the community. Hence, it is shown by the analysis that vaccination program, diagnosis and treatment help to control the TB dynamics. In furtherance to that, it is shown that preference should be given to diagnosis over treatment as diagnosis precedes treatment. It is as well shown that at lower vaccination rate (0–20%), TB would still be endemic in the population. As such, high vaccination rate is required to send TB out of the community.
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    The role of vaccination in curbing tuberculosis epidemic
    (Modeling Earth Systems and Environment, 2019-09-13) Ayinla, Ally Yeketi; Othman, Wan Ainun Mior; Omar Awang, M.A.
    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.