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    Mathematical model for the control of measles
    (African Journals Online (AJOL), 2018-05-03) O. J. Peter; O. A. Afolabi; A. A. Victor; C. E. Akpan; F. A. Oguntolu
    We proposed a mathematical model of measles disease dynamics with vaccination by considering the total number of recovered individuals either from natural recovery or recovery due to vaccination. We tested for the existence and uniqueness of solution for the model using the Lipchitz condition to ascertain the efficacy of the model and proceeded to determine both the disease free equilibrium (DFE) and the endemic equilibrium (EE) for the system of the equations and vaccination reproduction number are given. Numerical simulation of the model shows that vaccination is capable of reducing the number of exposed and infectious population.
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    Mathematical Modeling of Polio Virus Infection Incorporating Immigration and Vaccination
    (Faculty of Physical Sciences, University of Ilorin, 2019-12-01) G. Bolarin; I. U. Omatola; A. Yusuf; C. E. Odo; F. A. Oguntolu; M. A. Philip
    A deterministic mathematical model for polio infection dynamics with emphasis on immigration and vaccination was formulated and analyzed. We derived the basic reproduction number, of the model formulated. The effective reproduction number was computed using the next generation matrix to enable a qualitative analysis to be carried out on the model. Also, the disease-free equilibrium and endemic equilibrium points were computed. On analyzing the equilibrium points, we found that the disease-free equilibrium point is locally asymptotically stable if and the condition for existence on an Endemic Equilibrium point was also established. More so, numerical simulations showed that vaccination coverage of about 75% would be enough to eradicate polio from the population.
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    Analysis and Dynamics of Tuberculosis Outbreak: A Mathematical Modelling Approach
    (Advances in Systems Sciences and Applications (ASSA), 2022-12-30) Oguntolu, Festus Abiodun; Peter, Olumuyiwa James; Oshinubi, Kayode; Ayoola, Tawakalt Abosede; Oladapo, Asimiyu Olalekan; Ojo, Mayowa Michael
    Tuberculosis (TB) is an infectious disease caused by mycobacterium disease which causes major ill health in humans. Control strategies like vaccines, early detention, treatment and isolation are required to minimize or eradicate this deadly pandemic disease. This article presents a novel mathematical modelling approach to tuberculosis disease using Vaccinated-Susceptible-Latent-Mild-Chronic-Isolated-Treated model. We examined if the epidemiology model is well posed and then obtained two equilibria points (disease free and endemic equilibrium). We also showed that TB disease free equilibrium is locally and globally asymptotically stable if . We solved the model analytically using Homotopy Perturbation Method (HPM) and the graphical representations and interpretations of various effects of the model parameters in order to measure the impact for effective disease control are presented. The findings show that infected populations will be reduced when the isolation and treatment rates and their effectiveness are high.
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    Modeling tuberculosis dynamics with vaccination and treatment strategies
    (Elsevier BV, 2025-03-19) Olumuyiwa James Peter; Dipo Aldila; Tawakalt Abosede Ayoola; Ghaniyyat Bolanle Balogun; Festus Abiodun Oguntolu
    Tuberculosis (TB) remains a leading cause of morbidity and mortality worldwide, worsened by the emergence of drug-resistant strains. The implementation of vaccination and observed treatment still becomes the most popular intervention in many countries. This study develops a mathematical model to analyze TB dynamics by considering the impact of integrated intervention vaccination and treatment strategy, and also taking into account the possibility of treatment failure and drug–resistant. The model constructed by dividing the population into six compartments: susceptible S, vaccinated V, latent L, active TB (I), drug-resistant TB Dr, and recovered R. Through a mathematical analysis of the dynamical properties of the proposed model, we demonstrated that the disease-free equilibrium point is always locally asymptotically stable when the basic reproduction number is less than one and unstable when it exceeds one. Moreover, the endemic equilibrium point is shown to exist uniquely only when the basic reproduction number is greater than one, and once it exists, it is always locally stable. For better visualization of the stability properties, we perform continuation simulations to generate a bifurcation diagram of our model, utilizing various bifurcation parameters. The Partial Rank Correlation Coefficient (PRCC) approach is used to carry out sensitivity analyses to determine the most sensitive parameters to the disease control. Simulation results show that increased vaccination rates efficiently reduce the susceptible population to increase the vaccinated population, decreasing disease transmission and lowering the burden of active and drug-resistant tuberculosis. Recovery rates after second-line treatment have a substantial impact on the dynamics of drug-resistant tuberculosis. Higher recovery rates result in faster rises in the recovered population and improved disease control. The findings emphasize the need for integrated measures, such as vaccination campaigns and enhanced treatment procedures, to reduce tuberculosis incidence, minimize drug resistance, and improve public health outcomes. These findings lay the groundwork for enhancing tuberculosis control programs, especially in countries with limited resources.