Browsing by Author "Odetunde, O."
Now showing 1 - 7 of 7
Results Per Page
Sort Options
Item Global Stability Analysis of Sir Epidemic Model with Relapse and Immunity Loss(International Journal of Applied Science and Mathematical Theory ISSN 2489-009X Vol. 2 No.1 2016 www.iiardpub.org, 2016) Akinyemi, S. T; Ibrahim, M. O.; Usman, I. G.; Odetunde, O.A deterministic mathematical model for the transmission dynamics of infectious disease with immunity loss and relapse was built and analyzed. The model was shown to exhibit two equilibria, namely, a disease free equilibrium and an endemic equilibrium. The computated basic reproductive number (R_0) was used to establish that whenever R_0<1, the disease free equilibrium is locally asymptotically stable and the endemic equilibrium is locally asymptotically stable whenever R_0>1. Furthermore the global stability for the two equilibria was investigated using Lyapunov function. The model was simulated numerically to validate the analytical results.Item Mathematical analysis of a staged progression HIV/AIDS model with screening and drug resistance(ABACUS. 43(2) 162 – 179. Published by the Mathematical Association of Nigeria, 2016) Akinyemi, S. T; Ibrahim, M. O.; Moses, M. A.; Edogbanya, H. O.; Odetunde, O.In this paper, a staged progression model for HIV/AIDS transmission dynamics in the presence of screening and drug resistance is developed and rigorously analyzed. The model consist of eight mutually exclusive subpupolations with two equilibria, namely the disease free and endemic equilibrium. The disease free equilibrium is shown to be globally asymptotically stable whenever the effective reproduction number is less than unity by constructing Lyapunov function. Using the Kranoselski sublinearity trick and Lyapunov function, the endemic equilibrium for a special case was establish to be locally and globally asymptotically stable respectively when its associated effective reproduction number exceeds unityItem Mathematical modeling of Hepatitis B transition to primary liver cancer with consideration of partial immunity.(Journal of the Nigerian Association of Mathematical Physics 32 211 – 220. Published by the Nigerian Association of Mathematical Physics., 2015) Odetunde, O.; Ibrahim, M. O.; Lawal, J.; Edogbanya, H. O.; Akinyemi, S. TThis work study the rate of progression of Hepatitis B to Primary Liver Cancer, the effect of therapeutic treatment on the HBV and the role of vaccination of pregnant women as passive immunity for the unborn child. The equilibria states of both the disease free and the endemic were calculated. Positivity of the solution of the model was analyzed and the effective reproduction number was computed. The analysis of the reproduction number at the DFE indicated a substantial decrease in the number of secondary infection rate as a result of passively acquired immunity of the infant and the therapeutic treatment now available to HBV. However, the study show that the rate of progression to primary liver cancer (PLC) will be on the increase if the treatment is not affordable to all HBV patientsItem On the stability analysis of infectious model with therapy(Journal of the Nigerian Association of Mathematical Physics 32, 221 – 228. Published by the Nigerian Association of Mathematical Physics, 2015) Ayoade, A. A.; Ibrahim, M. O.; Edogbanya, H. O; Odetunde, O.; Akinyemi, S. TItem Optimal Control Analysis of Effect of HAART On Immune Cells Against HIV Infection. Advances in Mathematics(Advances in Mathematics Scientific Journal 7 (2), 89–107, 2018) Odetunde, O.; Lawal, J.; Edogbanya, H. O; Ibrahim, M. O.A non-linear deterministic mathematical model for the transmission dynamics of HIV infection within the body system of an infected individual was formulated for analysis. Multiplication of the virus at the detriment of the immune system of the body (notably the CD4-T-cells and Macrophages) is the effect of introduction of small amount of the virus into the body system of previously susceptible individual. The study aimed at looking into the effect of education, early diagnosis of the infection through proper screening and early treatment of the body as a means of helping the body to stay healthier for a longer period of time. The model developed was analysed for existence of solution, equilibria states (Infection Free Equilibrium I.F.E and Endemic State Equilibrium E.S.E). Local and Global Analysis of the effective reproduction number was done and the result shows that I.F.E is both locally and globally stable if R0 < 1 otherwise the infection spreads in the body. The optimal effect of using Highly Active Anti-Retrovirus Therapy (HAART) as an improved means to ART was considered. The result show that HAART is capable of removing the infected cells quicker thereby reducing the viral burden of the infection in the immune system.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 immunityItem Sensitivity analysis applied to the progression (deterioration) rate of Hepatitis B to primary liver cancer.(Journal of Mathematical Sciences 4(1) 907 – 918. Published by the National Mathematical Centre, Abuja, 2016) Odetunde, O.; Ibrahim, M. O.We aimed at studying the sensitivity analysis of the parameters to the effective reproduction number for the rate of progression of Hepatitis B virus (HBV) to primary liver cancer. The effect of vaccination , sensitization and proper education on HBV transmission was considered as control strategies on the transmission rate of the disease. Also, the effect of therapeutic treatment was considered on the rate at which the the patients living with HBV progresses to a primary liver cancer patients. Positivity of solution of the model as well as the disease free equilibrium and endemic equilibrium states of the model were discussed.Threshold analysis of some of the parameters were analysed and discussed.