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    Stability and optimal control analysis of an SCIR epidemic model
    (SCIK Publishing Corporation, 2020-10-16) Olumuyiwa James Peter; Ratchada Viriyapong; Festus Abiodun Oguntolu; Pensiri Yosyingyong; Helen Olaronke Edogbanya; Michael Oyelami Ajisope
    In this paper, we proposed a deterministic model of SCIR governed by a system of nonlinear differential equations. Two equilibria (disease-free and endemic) are obtained and the basic reproduction number R0 is calculated. If R0 is less than one, then the disease-free equilibrium state is globally stable i.e. the disease will be eradicated eventually. However, when R0 is greater than unity, the disease persists and the endemic equilibrium point is globally stable. Furthermore, the optimal control problem is applied into the model. The focus of this study is to determine what control method can be implemented to significantly slow the incidence of the epidemic disease, therefore we take into account various possible combinations of such three controls which are prevention via proper hygiene, screening of the infected carriers which enable them to know their health conditions and to go for early treatment and treatment of the infected individuals. The possible strategies of using combinations of the three controls on the spread of the disease, one at a time or two at a time is also discussed. Our numerical analysis of the optimal approach suggests that the best method is to incorporate all three controls in order to control the disease epidemic.
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    Stability Analysis of Disease Free Equilibrium (DFE) State of a Mathematical Model of Yellow Fever Incorporating Secondary Host
    (Pacific Journal of Science and Technology, 2017-12-28) Somma, Samuel Abu; Akinwande, N. I.; Jiya, M.; Abdulrahaman, S.
    In this paper we formulate a mathematical model of yellow fever incorporating secondary host. We obtained the Disease Free Equilibrium (DFE) Points and compute the basic reproduction number. The local and global stability of the DFE was analyzed using Jacobian Matrix stability techniques and Lyapunov function respectively. The local and global stability was asymptotically stable if 1 0 R  and 1 0 R  , respectively. The basic reproduction number and control parameters of the model were presented graphically.
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    Local Stability Analysis of a River Blindness Disease Model with Control
    (Pacific Journal of Science and Technology, 2018-05-22) Oguntolu, F. A.; Bolarin, G.; Somma, Samuel Abu; Bello, A. O.
    In this paper, a mathematical model to study the dynamics of River Blindness is presented. The existence and uniqueness of solutions of the model were examined by actual solution. The effective reproduction number was obtained using the next generation matrix. The Disease Free Equilibrium (DFE) State was obtained and analysed for stability. It was found that, the DFE State is Locally Asymptotically Stable (LAS) if the effective unstable if reproduction number R 0  1 . R 0  1 and