School of Physical Sciences (SPS)

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School of Physical Sciences (SPS)

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Author: search.filters.author.F.A. OguntoluSubject: search.filters.subject.Bifurcation

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    Mathematical Analysis of the Transmission Dynamics of Hepatitis B Virus
    (Springer Science and Business Media LLC, 2025-05-15) F.A. Oguntolu; O.J. Peter; D. Aldila; G. B. Balogun; O. P. Ogunmola; B. I. Omede
    Hepatitis B is a life-threatening hepatic illness induced by the Hepatitis B virus (HBV). This is a major worldwide health issue, especially in low- and middle-income nations in Africa and the Western Pacific, where prevalence rates are the greatest. Nevertheless, the existence of an efficacious vaccination, Hepatitis B persists in inflicting significant morbidity and death owing to a deficiency of awareness regarding the illness. Thus, we developed a deterministic mathematical model to elucidate the transmission dynamics of Hepatitis B, integrating elements such as vertical transmission, re-infection, and environmental viral concentration. The study starts with the calculation of the basic reproduction number and the assessment of the local stability of the disease-free equilibrium employing the Routh-Hurwitz criteria. A comprehensive examination of the model indicates that the model may experience backward bifurcation phenomena under some specific conditions. This trait presents considerable challenges in the proper management of Hepatitis B infection among the population. Assuming no re-infection of Hepatitis B post-recovery, the disease-free equilibrium point is globally asymptotically stable when the basic reproduction number is less than or equal to one. The sensitivity analysis of the basic reproduction number was conducted to assess the influence of each fundamental parameter in the model that contributes to disease transmission. Utilizing the optimal control theory to effectively curb the spread of Hepatitis B, we incorporated two time-varying control strategies, namely the prevention of susceptible individuals from acquiring HBV (through safe sex practice, regular washing of hands, and using protective hand gloves when handling blood, body fluid and semen) and the sensitization on individuals on personal hygiene, sterilization and proper disposal of medical and dental equipment like syringes in order to reduce the shedding of HBV in the environment. The numerical simulations indicated that Hepatitis B infection may be effectively managed and mitigated within the community if both control measures are correctly implemented.
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    Mathematical model of COVID-19 transmission dynamics incorporating booster vaccine program and environmental contamination
    (Elsevier BV, 2022-11) N.I. Akinwande; T.T. Ashezua; R.I. Gweryina; S.A. Somma; F.A. Oguntolu; A. Usman; O.N. Abdurrahman; F.S. Kaduna; T.P. Adajime; F.A. Kuta; S. Abdulrahman; R.O. Olayiwola; A.I. Enagi; G.A. Bolarin; M.D. Shehu
    COVID-19 is one of the greatest human global health challenges that causes economic meltdown of many nations. In this study, we develop an SIR-type model which captures both human-to-human and environment-to-human-to-environment transmissions that allows the recruitment of corona viruses in the environment in the midst of booster vaccine program. Theoretically, we prove some basic properties of the full model as well as investigate the existence of SARS-CoV-2-free and endemic equilibria. The SARS-CoV-2-free equilibrium for the special case, where the constant inflow of corona virus into the environment by any other means, Ω is suspended (Ω=0) is globally asymptotically stable when the effective reproduction number 𝑅0⁢𝑐<1 and unstable if otherwise. Whereas in the presence of free-living Corona viruses in the environment (Ω>0), the endemic equilibrium using the centre manifold theory is shown to be stable globally whenever 𝑅0⁢𝑐>1. The model is extended into optimal control system and analyzed analytically using Pontryagin's Maximum Principle. Results from the optimal control simulations show that strategy E for implementing the public health advocacy, booster vaccine program, treatment of isolated people and disinfecting or fumigating of surfaces and dead bodies before burial is the most effective control intervention for mitigating the spread of Corona virus. Importantly, based on the available data used, the study also revealed that if at least 70% of the constituents followed the aforementioned public health policies, then herd immunity could be achieved for COVID-19 pandemic in the community.