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Start date: 2023Subject: search.filters.subject.Stability

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    Mathematical model and analysis of the soil-transmitted helminth infections with optimal control
    (Springer Science and Business Media LLC, 2024-02) Festus Abiodun Oguntolu; Olumuyiwa James Peter; Abubakar Yusuf; B. I. Omede; G. Bolarin; T. A. Ayoola
    Soil-transmitted helminth diseases are highly prevalent in impoverished regions and pose a significant health burden on the global population. These diseases are primarily transmitted through the contamination of soil with human faces containing parasite eggs. This study presents a novel deterministic mathematical model to comprehensively investigate the dynamics of helminth infection transmission through the soil. The mathematical model exhibits two equilibrium points: the diseases-free equilibrium point (DFE) and the endemic equilibrium point (EEP). The DFE is proven to be locally and globally asymptotically stable when the basic reproduction number is less than one, indicating the potential for disease eradication. Conversely, the EEP is locally asymptotically stable when the basic reproduction number exceeds unity, representing a persistent endemic state. To explore effective intervention strategies for controlling the spread of these infections, optimal control theory is applied. The study incorporates two time-varying control variables derived from sensitivity analysis: the rate of hygiene consciousness in the susceptible class and the rate of hygiene consciousness in the infectious class. Numerical simulations demonstrate that implementing optimal control strategies can successfully curb and mitigate soil-transmitted helminth infections. Overall, this research highlights the importance of proactive and targeted interventions, emphasizing the significance of hygiene education and awareness campaigns. By implementing optimal control measures based on the proposed strategies, the burden of soil-transmitted helminth diseases can be significantly reduced, improving public health in affected regions.
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    On the verification of existence of backward bifurcation for a mathematical model of cholera dynamics
    (African Journals Online, 2023-09-12) A. A. Ayoade; O. J. Peter; F. A. Oguntolu; C.Y. Ishola; S. Amadiegwu
    A cholera transmission model, which incorporates preventive measures, is studied qualitatively. The stability results together with the center manifold theory are used to investigate the existence of backward bifurcation for the model. The epidemiological consequence of backward bifurcation is that the disease may still persist in the population even when the classical requirement of the reproductive number being less than one is satisfied.
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    Modelling the impacts of media campaign and double dose vaccination in controlling COVID-19 in Nigeria
    (Elsevier BV, 2023-10) N.I. Akinwande; S.A. Somma; R.O. Olayiwola; T.T. Ashezua; R.I. Gweryina; F.A. Oguntolu; O.N. Abdurahman; F.S. Kaduna; T.P. Adajime; F.A. Kuta; S. Abdulrahman; A.I. Enagi; G.A. Bolarin; M.D. Shehu; A. Usman
    Corona virus disease (COVID-19) is a lethal disease that poses public health challenge in both developed and developing countries of the world. Owing to the recent ongoing clinical use of COVID-19 vaccines and non-compliance to COVID-19 health protocols, this study presents a deterministic model with an optimal control problem for assessing the community-level impact of media campaign and double-dose vaccination on the transmission and control of COVID-19. Detailed analysis of the model shows that, using the Lyapunov function theory and the theory of centre manifold, the dynamics of the model is determined essentially by the control reproduction number (Rmv). Consequently, the model undergoes the phenomenon of forward bifurcation in the absence of the double dose vaccination effects, where the global disease-free equilibrium is obtained whenever Rmv≤1. Numerical simulations of the model using data relevant to the transmission dynamics of the disease in Nigeria, show that, certain values of the basic reproduction number ((R0≥7)) may not prevent the spread of the pandemic even if 100% media compliance is achieved. Nevertheless, with assumed 75% (at R0=4)) media efficacy of double dose vaccination, the community herd immunity to the disease can be attained. Furthermore, Pontryagin's maximum principle was used for the analysis of the optimized model by which necessary conditions for optimal controls were obtained. In addition, the optimal simulation results reveal that, for situations where the cost of implementing the controls (media campaign and double dose vaccination) considered in this study is low, allocating resources to media campaign-only strategy is more effective than allocating them to a first-dose vaccination strategy. More so, as expected, the combined media campaign-double dose vaccination strategy yields a higher population-level impact than the media campaign-only strategy, double-dose vaccination strategy or media campaign-first dose vaccination strategy.