Browsing by Author "Ayinla, Ally Yeketi"

Now showing 1 - 7 of 7
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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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    Integrated Collocation Approximation Methods for Solving High Order Ordinary Differential Equations
    (Journal of the Nigerian Association of Mathematical Physics, 2017-09) Ayinla, Ally Yeketi; Ogunniran, Muhyideen O.; Odetunde, Opeyemi
    This work deals with integrated collocation approximation methods for solving high order ordinary differential equations by Chebyshev polynomials and power series bases functions. The assumed approximate solution in terms of Chebyshev polynomials and power series are substituted into the general high order ordinary differential equations considered. Thus, after simplification, the resulting equation is then collocated for both cases and thus resulted into algebraic linear system of equations which are then solved by Mathematica 5.2 to obtain the unknown constants involved in the approximate solution. The methods are illustrated on three examples. The results obtained in terms of absolute errors are tabulated for comparison. From the tables of results, we observed that Chebyshev polynomials approximation gives better result for all cases of N (i.e. the degree of approximant) in the work.
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    A mathematical analysis of the tuberculosis epidemic
    (Mathematical Analysis and Optimization Research Group, 2020-12-03) Ayinla, Ally Yeketi
    Long latency period has been seen as a major setback in the control of tuberculosis (TB), because an individual infected of TB can be latent for years. In this paper, a four compartment deterministic model is presented to change the narrative. It is established that making sure every individual infected of TB pass through the latent stage would actually reduce the TB incident rate. Also established from the model is that prevention against TB re-infection has no significant contribution to the disease incident rate, which implies the money meant to guard against TB reinfection should not be wasted. The formulated model was shown to be locally asymptotically stable at the disease free equilibrium (DFE) whenever R_0 < 1 and the global asymptotic stability (GAS) at this point was as well established. It is as well shown that the endemic equilibrium point (EEP) is locally asymptotically stable with the aid of phase portrait and the GAS of the EEP was established by defining a suitable Lyapunov function.
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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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    A Mathematical Model on Marburg Virus Disease
    (Nigerian Journal of Mathematics and Applications, 2022) Ayinla, Ally Yeketi; Ayinla, Abdulquadri Yeketi
    This research discusses the management of Marburg virus disease (MVD) using a mathematical model. The formulated model consists of five (5) mutually exclusive compartments. The local and global stability of the DFE of the formulated model is established. Subsequently, it is shown that the effective management of the disease depends greatly on the incubation period and exposure to the infection. The more the incubation period, the greater the chances of disease incidence reduction.
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    ROLE OF REINFECTION IN TRANSMISSION DYNAMICS OF COVID-19: A SEMI-ANALYTICAL APPROACH USING DIFFERENTIAL TRANSFORM METHOD
    (Malaysian Journal of Computing, 2021-03-02) Odetunde, Opeyemi; Jibril, Lawal; Ayinla, Ally Yeketi
    Reinfection of a recovered individual either as a result of relapse or new contact no doubt poses a major threat to the eradication of an infection within the host community. In this work, the role of re-infection in the transmission dynamics of COVID-19 was considered and analysed using the semi-analytical tool Differential Transform Method (DTM). COVID-19 (also known as Coronavirus) has shut down the economy of the world since it became a global pandemic. A mathematical model was constructed with consideration of multiple pathways of infection transmission, the treatment strategies and policies adopted (social distancing, wearing of face mask and so on) to limit the spread of the infection globally. The non-linear system of equations governing the model was solved using DTM and the resulting series solution was compared with the standard numeric Runge-Kutta order 4 (RK4). It was discovered that re-integration of a recovered individual into the susceptible community without observing the prevention guidelines such as social distancing, washing of hands and proper sanitizing could increase the spread of the infection since the recovered individuals are not guaranteed of immunity against the infection after recovery. The study concluded that families of recovered patients must ensure adequate preventive measure while integrating their recovered loved ones back to their midst.
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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.