Industrial Mathematics
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Industrial Mathematics
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Item Mathematical Modeling on the Transmission Dynamics of HIV and Hepatitis B (HBV) Co‐Infection in the United States(Wiley, 2025-06-26) F. A. Oguntolu; O. J. Peter; D. Aldila; G. B. Balogun; A. O. Ajiboye; B. I. OmedeHuman immunodeficiency virus (HIV) and hepatitis B virus (HBV) are major public health concern worldwide, contributing to significant morbidity and mortality. Managing co-infection between HIV and HBV presents additional challenges in clinical treatment and patient outcomes. In this article, we developed a comprehensive co-infection model to explore the complex transmission dynamics between HIV and HBV in the United States. Our model incorporates crucial factors such as infection through birth or migration, HBV vaccination, and the possibility of reinfection following HBV recovery. Our mathematical analysis started with the analysis of the two non-co-infection submodels, that is, for HIV-only and HBV-only models. We derived the basic reproduction number for each submodel and applied the Routh-Hurwitz criterion to assess the local stability of their respective disease-free equilibrium points. Our investigation revealed that the HIV-only submodel is globally asymptotically stable when its basic reproduction number remains below one. Conversely, the HBV-only submodel exhibits a backward bifurcation, meaning that both disease-free and endemic equilibrium states can coexist even when the reproduction number falls below one. This phenomenon complicates HBV control strategies under such conditions. However, in the absence of reinfection, the HBV-only model reaches global stability at the disease-free equilibrium whenever its reproduction number is below one. Using center manifold theory, we further demonstrated that the full HIV-HBV co-infection model also undergoes backward bifurcation. A sensitivity analysis was conducted on the basic reproduction numbers of HIV and HBV to identify critical parameters influencing the transmission dynamics of both infections. Our results indicate a positive correlation between the spread of one infection and the prevalence of the other. Additionally, we validated the model by fitting it to annual cumulative data on new HIV cases and reported acute HBV infections in the United States. Numerical simulations suggest that increasing condom use adherence, enhancing treatment coverage for both infections, and boosting HBV vaccination rates can substantially reduce the prevalence of HIV, HBV, and their co-infection.Item Direct and Indirect Transmission Dynamics of Typhoid Fever Model by Differential Transform Method(ATBU, Journal of Science, Technology & Education (JOSTE), 2018-03) O. J. Peter; M. O. Ibrahim; F. A. Oguntolu; O. B. Akinduko; S. T. AkinyemiThe aim of this paper is to apply the Differential Transformation Method (DTM) to solve typhoid fever model for a given constant population. This mathematical model is described by nonlinear first order ordinary differential equations. First, we find the solution of this model by using the differential transformation method (DTM). In order to show the efficiency of the method, we compare the solutions obtained by DTM and RK4. We illustrated the profiles of the solutions, from which we speculate that the DTM and RK4 solutions agreed well.Item Approximate Solution of Typhoid Fever Model by Variational Iteration Method(ATBU, Journal of Science, Technology & Education (JOSTE), 2018-09) A. F. Adebisi; O. J. Peter; T. A. Ayoola; F. A. Oguntolu; C. Y. IsholaIn this paper, a deterministic mathematical model involving the transmission dynamics of typhoid fever is presented and studied. Basic idea of the disease transmission using compartmental modeling is discussed. The aim of this paper is to apply Variational Iteration Method (VIM) to solve typhoid fever model for a given constant population. This mathematical model is described by nonlinear first order ordinary differential equations. First, we find the solution of the model by using Variation Iteration Method (VIM). The validity of the VIM in solving the model is established by classical fourth-order Runge-Kutta method (RK4) implemented in Maple 18. In order to show the efficiency of the method we compare the solutions obtained by VIM and RK4. We illustrated the profiles of the solutions of each of the compartments, from which we speculate that the VIM and RK4 solutions agreed well.Item Mathematical model for the control of measles(African Journals Online (AJOL), 2018-05-03) O. J. Peter; O. A. Afolabi; A. A. Victor; C. E. Akpan; F. A. OguntoluWe proposed a mathematical model of measles disease dynamics with vaccination by considering the total number of recovered individuals either from natural recovery or recovery due to vaccination. We tested for the existence and uniqueness of solution for the model using the Lipchitz condition to ascertain the efficacy of the model and proceeded to determine both the disease free equilibrium (DFE) and the endemic equilibrium (EE) for the system of the equations and vaccination reproduction number are given. Numerical simulation of the model shows that vaccination is capable of reducing the number of exposed and infectious population.Item Multi-Step Homotopy Analysis Method for Solving Malaria Model(Universiti Sultan Zainal Abidin (Malaysian Journal of Applied Sciences), 2018-12-30) O. J. Peter; A. F. Adebisi; F. A. Oguntolu; S. Bitrus; C. E. AkpanIn this paper, we consider the modified epidemiological malaria model proposed by Abadi and Harald. The multi-step homotopy analysis method (MHAM) is employed to compute an approximation to the solution of the model of fractional order. The fractional derivatives are described in the Caputo sense. We illustrated the profiles of the solutions of each of the compartments. Figurative comparisons between the MHAM and the classical fourth-order reveal that this method is very effective.Item On the verification of existence of backward bifurcation for a mathematical model of cholera dynamics(African Journals Online, 2023-09-12) A. A. Ayoade; O. J. Peter; F. A. Oguntolu; C.Y. Ishola; S. AmadiegwuA cholera transmission model, which incorporates preventive measures, is studied qualitatively. The stability results together with the center manifold theory are used to investigate the existence of backward bifurcation for the model. The epidemiological consequence of backward bifurcation is that the disease may still persist in the population even when the classical requirement of the reproductive number being less than one is satisfied.