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    Mathematical model and analysis of the soil-transmitted helminth infections with optimal control
    (Springer Science and Business Media LLC, 2024-02) Festus Abiodun Oguntolu; Olumuyiwa James Peter; Abubakar Yusuf; B. I. Omede; G. Bolarin; T. A. Ayoola
    Soil-transmitted helminth diseases are highly prevalent in impoverished regions and pose a significant health burden on the global population. These diseases are primarily transmitted through the contamination of soil with human faces containing parasite eggs. This study presents a novel deterministic mathematical model to comprehensively investigate the dynamics of helminth infection transmission through the soil. The mathematical model exhibits two equilibrium points: the diseases-free equilibrium point (DFE) and the endemic equilibrium point (EEP). The DFE is proven to be locally and globally asymptotically stable when the basic reproduction number is less than one, indicating the potential for disease eradication. Conversely, the EEP is locally asymptotically stable when the basic reproduction number exceeds unity, representing a persistent endemic state. To explore effective intervention strategies for controlling the spread of these infections, optimal control theory is applied. The study incorporates two time-varying control variables derived from sensitivity analysis: the rate of hygiene consciousness in the susceptible class and the rate of hygiene consciousness in the infectious class. Numerical simulations demonstrate that implementing optimal control strategies can successfully curb and mitigate soil-transmitted helminth infections. Overall, this research highlights the importance of proactive and targeted interventions, emphasizing the significance of hygiene education and awareness campaigns. By implementing optimal control measures based on the proposed strategies, the burden of soil-transmitted helminth diseases can be significantly reduced, improving public health in affected regions.
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    Modeling prevalence of meningitis control strategies through evaluating with available data on meningitis cases reported in Nigeria
    (Springer Science and Business Media LLC, 2025-05-14) O.J. Peter; F.A. Oguntolu; N. Nyerere; A. El-Mesady
    Meningitis is a major public health concern, especially in developing nations, due to its devastating consequences for human health. Although modeling studies have examined disease transmission dynamics, little attention has been paid to how control strategies affect the behavior of different population groups, including carriers, symptomatic individuals, hospitalized patients, and those in intensive care. This study proposes a computational framework that compares the effectiveness of vaccination of people at risk of the disease versus treating symptomatic infected persons. The basic reproduction number is used to evaluate the equilibrium points. Assess the precision of the proposed model’s illustration to data. We fit the meningitis model using the information at our disposal on meningitis cases reported in Nigeria from the first week of January to the last week of December 2023; this was obtained from the Nigerian Center for Disease Control (NCDC) database. We also performed a sensitivity analysis using a normalized forward sensitivity index to see which parameters had significant effects on the effective reproduction number. The results of both analytical techniques and numerical simulations reveal that recruitment rate, vaccination, progression from carrier to symptomatic stages, and disease-induced death all significantly reduce the incidence and prevalence of meningitis in the community. The study findings could be used to inform decisions about meningitis control initiatives.
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    Mathematical model for the control of lymphatic filariasis transmission dynamics
    (SCIK Publishing Corporation, 2021-02-23) Festus Abiodun Oguntolu; Gbolahan Bolarin; Olumuyiwa James Peter; Abdullah Idris Enagi; Kayode Oshinubi
    In this paper, a mathematical model for the transmission dynamics of lymphatic filariasis is presented by incorporating the infected without symptom, the infected with symptom and treatment compartments. The model is shown to have two equilibrium states: the disease-free equilibrium (DFE) and the endemic equilibrium states. An explicit formula for the effective reproduction number was obtained in terms of the demographic and epidemiological parameters of the model. Using the method of linearization, the disease-free equilibrium state was found to be locally asymptotically stable if the basic reproduction number is less than unity. By constructing a suitable Lyapunov function, the disease-free equilibrium state was found to be globally asymptotically stable. This means that lymphatic filariasis could be put under control in a population when the effective reproduction number is less than one. The endemic equilibrium state was found to be locally asymptotically stable. By constructing yet another Lyapunov function, the endemic equilibrium state was found to be globally asymptotically stable under certain conditions. Sensitivity analysis was carried out on the effective reproduction number, the most sensitive parameters were the treatment rate of human population and the infected rate of human population. Results from the simulation carried out showed that treatment level coverage of human population should target a success rate of 75% for LF to be under control in the population.