Browsing by Author "Dotia, A. K."
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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 Optimal Control Analysis of HIV/AIDS Model with PrEP Strategy and Behavioral Changes(2025-04-10) Ahmed, B. M.; Dotia, A. K.; Ibrahim, M. O.; Adeoye, A. O.; Ejieji, C. N.; Olotu, O. T.; Bakare, G. N.; Adama, P. W.; Romanus, N.Combining Pre-Exposure Prophylaxis (PrEP) with behavioral strategies has become vital in curbing HIV/AIDS transmission, offering a pathway to reduce infections and allocate health resources more effectively. In this study, we developed a six-compartment mathematical model to analyze the spread and control of HIV/AIDS. Through rigorous analysis, we calculated the basic reproduction number (R₀) to assess transmission potential and evaluated the stability of the disease-free equilibrium state. To identify optimal strategies for reducing HIV/AIDS prevalence, we designed an optimal control framework using Pontryagin’s Minimum Principle. This approach allowed us to evaluate the effectiveness of prevention tactics such as public health education, condom use, screening, and treatment both individually and in combination. Our findings highlight that pairing community awareness campaigns with increased condom usage among adults, alongside proactive screening and treatment programs, significantly reduces new infections and overall prevalence. Numerical simulations further demonstrated how these measures lower infection rates, aligning with our theoretical predictions. These insights emphasize the importance of integrated, multi-pronged interventions to guide public health policies and resource distribution in the fight against HIV/AIDS.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 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.