Browsing by Author "Ibrahim, M.O."
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Item A Graph-Theoretic Method on HBY Epidemic Model(Bulletin of the Science Association of Nigeria, 2019) Dotia, A.K.; Zubair, O.R.; Moshood, A.R.; Ibrahim, M.O.; Abubakar, Jos U.In this paper, we present an epidemic model with non-monotonic incidence function. This epidemic model is investigated for different classes of infectious diseases. Mathematical analyses are carried out to determine the positivity of solution and the Graph-Theoretic method is used in calculating the Basic reproduction number. In addition, we obtained the numerical simulation to verify the model predictions. The results suggested that the model is approaching equilibrium with increase immunization program.Item Optimal control approach on hepatitis B model with vaccinations(Journal of the Nigerian Association of Mathematical Physics, 2017-05) Dotia, A.K.; Ibrahim, M.O.; Abubakar, Jos U.We present a time-dependent HBV epidemic model with both prophylactic and therapeutic vaccination. This epidemic model is investigated for different classes of infectious diseases. Mathematical analyses are carried out, that determines the positivity of solution and an optimal control approach is applied in order to find the best way to fight the disease. An optimal control strategy in the form of vaccination, and to minimize or eradicate the mother to child transmission is used. The study concluded that both prophylactic and therapeutic vaccination are efficient ways to curb the epidemic.Item Radiative fluid flow over a vertical porous channel under optically thick approximation in the presence of MHD(Journal of the Nigerian Association of Mathematical Physics, 2014) Ibrahim, M.O.; Asogwa, K.K.; Uwanta, I.J.; Abubakar, Jos U.Numerous nonlinear equations that come up in real life situations defy analytical solutions; hence numerical methods are desirable to obtain the solutions of such equations. In this study, we use Newton scheme method from Taylor series to solve fourth order nonlinear problem. A mathematical software MATLAB was used to solve the system of equations to obtain the unknown constants. The velocity profiles and temperature profile are studied for different physical parameters like Magnetohydrodynamic M, porous term P, Radiation F and thermal Grashof number Ga. The results obtained after computation taking into cognizance the parameters present shows that the Magnetic and Porous parameters increase with increasing velocity, while the trend reverses with Radiation and thermal Grashof number under optically thick approximation.Item Reproduction Number of Vertical Transmission of Measles Model(A Journal of National Mathematical Centre, Abuja, 2014) Ibrahim, M.O.; Odetunde, O.; Ayoade, A.A.; Abubakar, Jos U.In this model, we study the reproduction number of measles epidemiology, the rate of vertical transmission of measles and antibodies, including the effect of maternal antibody on the spread of measles to the infant. We exempt the vaccinated class due to the finding of Viera Scheibner. We demonstrated that the disease will die out if the basic reproduction number for the disease free equilibrium R_{0}<1. This is the case of a disease free state, with no infection in the population. Otherwise, the disease may become endemic if the basic reproduction number is bigger than unity. The basic reproduction number at both the disease free state and the endemic state were obtained and the result shows stability in the effect of mother to child transmission of either disease or immunity