Industrial Mathematics

Permanent URI for this collectionhttp://197.211.34.35:4000/handle/123456789/188

Industrial Mathematics

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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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    Global Stability Analysis of Typhoid Fever Model
    (Advances in Systems Sciences and Applications (ASSA), 2020-06-30) Peter, Olumuyiwa James; Adebisi, Ajimot Folasade; Ajisope, Michael Oyelami; Ajibade, Fidelis Odedishemi; Abioye, Adesoye Idowu; Oguntolu, Festus Abiodun
    We analyze with four compartments a deterministic nonlinear mathematical model of typhoid fever transmission dynamics. Using the Lipchitz condition, we verified the existence and uniqueness of the model solutions to establish the validity of the model and derive the equilibria states of the model, i.e. disease-free equilibrium (DFE) and endemic equilibrium (EE). The computed basic reproductive number R0 was used to establish that the disease-free equilibrium is globally asymptotically stable when its numerical values are less than one while the endemic equilibrium is locally asymptotically stable when its values are greater than one. In addition, the Lyapunov function was applied to investigate the stability property for the (DFE). The model was numerically simulated to validate the results of the analysis.