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    Mathematical model for the control of infectious disease
    (African Journals Online (AJOL), 2018-05-03) O. J. Peter; O. B. Akinduko; F. A. Oguntolu; C. Y. Ishola
    We proposed a mathematical model of infectious disease dynamics. The model is a system of first order ordinary differential equations. The population is partitioned into three compartments of Susceptible S(t) , Infected I(t) and Recovered R(t). Two equilibria states exist: the disease-free equilibrium which is locally asymptotically stable if Ro < 1 and unstable if Ro > 1. Numerical simulation of the model shows that an increase in vaccination leads to low disease prevalence in a population.
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    Mathematical Modeling on the Transmission Dynamics of Diphtheria with Optimal Control Strategies
    (Department of Mathematics, Universitas Negeri Gorontalo, 2025-03-29) Festus Abiodun Oguntolu; Olumuyiwa James Peter; Benjamin Idoko Omede; Ghaniyyat Bolanle Balogun; Aminat Olabisi Ajiboye; Hasan S. Panigoro
    Diphtheria is an acute bacterial infection caused by Corynebacterium diphtheriae, characterized by the formation of a pseudo-membrane in the throat, which can lead to airway obstruction and systemic complications. Despite the availability of effective vaccines, diphtheria remains a significant public health concern in many regions, particularly in areas with low immunization coverage. In this study, we formulated and rigorously analyzed a deter ministic epidemiological mathematical model to gain insight into the transmission dynamics of Diphtheria infection, incorporating the concentration of Corynebacterium Diphtheriae in the environment. The analysis of the model begins with the computation of the basic reproduction number and the examination of the local stability of the disease-free equilibrium using the Routh-Hurwitz criterion. An in-depth analysis of the model reveals that the model undergoes the phenomenon of backward bifurcation. This characteristic poses significant hurdles in effectively controlling Diph theria infection within the population. However, under the assumption of no re-infection of Diphtheria infection after recovery, the disease-free equilibrium point is globally asymptotically stable whenever the basic reproduction num ber is less than one. Furthermore, the sensitivity analysis of the basic reproduction number was carried out in order to determine the impact of each of the model basic parameters that contribute to the transmission of the disease. Utilizing the optimal control theory to effectively curb the spread of Diphtheria, We introduced two time dependent control measures, to mitigate the spread of Diphtheria. These time dependent control measures represent preventive actions, such as public enlightenment campaign to sensitize and educate the general public on the dynamics of Diph theria and proper personal hygiene which includes regular washing of hands to prevent susceptible individuals from acquiring Diphtheria, and environmental sanitation practices such as cleaning of surfaces and door handle to reduced the concentration of Corynebacterium diphtheriae in the environment. The results from the numerical simulations reveal that Diphtheria infection can successfully be controlled and mitigated within the population if we can increase the vaccination rate and the decay rate of Corynebacterium Diphtheriae in the environment, as well as properly and effectively implementing these optimal control measures simultaneously.
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    Modified Maternally-Derived-Immunity Susceptible Infectious Recovered (MSIR) Model of Infectious Disease: Existence of Equilibrium and Basic Reproduction Number
    (Nigerian Journal of Technological Research, 2015-06-03) Somma, Samuel Abu; Akinwande, N. I.; Gana, P.; Abdulrahaman, S.; Ashezua, T. T.
    In this paper we modified the MSIR Model by adding the vaccination rate and death rate due to the disease to the existing MSIR model. We verified the positivity of the solution and obtained the Disease Free Equilibrium (DFE) of the model. We also determined the basic reproduction number using next generation Matrix and Jacobian matrix method.