Browsing by Author "Ibrahim, M. O."
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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 Global Stability of HBV Epidemic Model(Nigerian Association of Mathematical Physics, 2015-11-01) Dotia, A. K.; Ibrahim, M. O.; Bello, K. A.; Yisa, B. M.; Ahmed, B. M.In this paper, we present an hepatitis B model with multiple transmission ways of the acute counsel, uncounsel and carrier infection classes and derive basic reproduction number, which indicates that hepatitis B is endemic. Existence of disease free and endemic equilibrium state are carried-out. The disease free and endemic equilibrium are shown to be globally asymptotically stable. In addition, we obtained numerical simulation to verify the model predictions. The results suggest that the endemic nature of the model was stable. However, if the control measures put in place can be maximize, then the model can be used to predict the effectiveness of the prophylactic vaccination program in sustaining the population from the spread of the disease.Item Global Stability of HBV Epidemic Model(2015) Dotia, A. K.; Ibrahim, M. O.; Bello, K. A.; Yisa, B.M; Ahmed, B. M.In this paper, we present an hepatitis B model with multiple transmission ways of the acute counsel, uncounsel and carrier infection classes and derive the basic reproduction number, which indicates that hepatitis B is endemic. Existence of Disease Free and Endemic Equilibrium State are carried-out. The disease free and endemic equilibria are shown to be globally asymptotically stable. In addition, we obtained the numerical simulation to verify the model was predictions. The results suggest that the endemic nature of the model was stable. However, if the control measure put in place can be maximize, then the model can be use to predict the effectiveness of the prophylactic vaccination program in sustaining the population from the spread of the disease.Item A Graph-Theoretic Method for the Basic Reproduction Number in Age-Structured Hepatitis B Model(2019) Dotia, A. K.; Ibrahim, M. O.; Ejieji, C.N.; Bello, K. A.; Ahmed, B.M.; Ajanaku, B.K; Kazeem, A. B.; Lawan, A. O.In this paper, we present an Age-Structured hepatitis B model. This epidemic model is investigated for different classes of infectious diseases that can be transmitted through an effective contact with infective individuals, who are contagious. The Graph-Theoretic Method for the Basic Reproduction Number was obtained. In addition, the numerical simulation is used to virtually verify the model predictions. The result suggest that the endemic nature of the model is approaching equilibrium with increase immunization program and other control measures put in place.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 Mathematical Modelling of a Staged Progression HIV/AIDS Model with Control Measures(Journal of Nigerian Association of Mathematical Physics. Published by National Association of Mathematical Physics, 2015-03) Ibrahim, M. O.; Akinyemi, S. T.; Dago, M. M.; Bakare, G. N.A staged-progression model for HIV/AIDS transmission dynamics is formulated and analyzed to study the impact of condom usage, HIV-reated public health program and treatment. The local and global stability for the disease free equilibrium(DFE) was proved for Re <1 and Kransnoselki sublinearity trick was used to show that the endemic equlilibrium (EE) is locally asymptotically stable for a special case whenever Re1 >1. Numerical simulation was also carried out for both EE and EE at special case to illustrate the ideas of the results.Item 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 OPTIMAL CONTROL ON HEPATITIS B VIRUS MODEL WITH NON-MONOTONIC INCIDENCE FUNCTION(2019) Dotia, A. K.; Ibrahim, M. O.; Ejieji, C.N.; Bello, K. A.; Ahmed, B.M.; Ajanaku, B.; Kazeem, A. B.; Lawan, A. O.In this paper, a time- dependent model of prophylactic vaccination HBV is considered. This epidemic model is being investigated for various infectious disease classes, counsel and uncounsel. Mathematical analyzes are performed to determine the positivity and we applied an optimal control strategies in the form of vaccination to minimize or eradicate transmission from mother to child. The study concluded that prophylactic vaccination is not an efficient way to curb the epidemic.Item Optimal Test Strategies for HBV-HIV Co-Infection Model(2019) Dotia, A. K.; Ibrahim, M. O.; Ejieji, C. N.; Bello, K. A.; Ahmed, B. M.; Ajanaku, B.; Kazeem, A. B.; Lawan, A. O.In this paper, we present a deterministic model for the co-interaction of HBV and HIV in a population. Mathematical analyses are carried out, which determines the positivity of solution and optimal control. This study examined the effectiveness of the efforts put in place in eliminating the birth of prenatally infected chronic carrier mother, considering the efficacy of prophylactic vaccine against the incidence of new cases. The scheme shows that the disease can be resisted with vaccination(s) and treatment.Item 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.Item Stability Analysis of HBV Epidemic Model with Non - Monotonic Incidence Function(Nigerian Association of Mathematical Physics, 2015-11-01) Dotia, A. K.; Ibrahim, M. O.; Bello, K. A.; Yisa, B. M.; Ahmed, B. M.In this paper, we present an hepatitis B model with non-monotonic incidence function. The model, which is of the form of system of nonlinear differential equations, are constructed. This epidemic model is investigated for different classes of infectious diseases that can be transmitted through an effective contact with an infective individuals, who are contagious (symptomatic and asymptomatic carrier). Mathematical analysis are carried out, that determines the equilibria solutions and stability analysis of the equilibria of the model, using nonlinear Lyapunov function of Goh-Volterra type. In addition, we obtained the numerical simulation to verify the model predictions. The result suggest that the endemic nature of the model is approaching equilibrium with increase immunization program and other control measures put in place.