Mathematics

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Mathematics

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Author: search.filters.author.Ashezua, T. T.Has files: Yes

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    Mathematical analysis of a Chlamydia trachomatis with nonlinear incidence and recovery rates
    (Proceedings of 2nd International Conference on Mathematical Modelling, Optimization and Analysis of Disease Dynamics (ICMMOADD) 2025. Federal University of Technology, Minna, Nigeria, 2025-02-20) Ashezua, T. T.; Abu, E. A.; Somma, Samuel Abu
    Chlamydia, one of the commonest sexually transmitted infections (STIs), remain a public health concern in both underdeveloped and developed countries of the world. Chlamydia has caused worrying public health consequences hence much research work is needed to check the spread of the disease in the population. In this paper, a mathematical model for Chlamydia is developed and analyzed with nonlinear incidence and recovery rates. Qualitative analysis of the model shows that the disease-free equilibrium is locally asymptotically stable using the method of linearization. Further, using the comparison theorem method, the disease-free equilibrium is found to be globally asymptotically stable whenever the associated reproduction number is less than unity. Furthermore, mathematical analysis of the reproduction number shows that the intervention levels and the maximum per capita recovery rate due to effective treatment has a significant impact in reducing the burden of Chlamydia in the population. Numerical results show a relationship between the transmission rate, intervention levels, maximum per capita recovery rate and the reproduction number. Sensitivity analysis was conducted on the parameters connected to the reproduction number, Rc and results reveal that the top parameters that significantly drive the dynamics of Chlamydia in the population are the transmission rate, intervention levels and the maximum per capita recovery rate. These parameters need to be checked by healthcare policy makers if the disease must be controlled in the population.
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    An Appraisal on the Application of Reproduction Number for the Stability Analysis of Disease - Free Equilibrium State for S-I-R Type Models
    (Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD) 2024, 2024-02-28) Abdurrahman, Nurat Olamide; Somma S. A.; Akinwande, N. I.; Ashezua, T. T.; Gweryina, R.
    One of the key ideas in mathematical biology is the basic reproduction number, which can be utilized to comprehend how a disease epidemic profile might evolve in the future. The basic reproduction number, represented by R0 , is the anticipated number of secondary cases that a typical infectious individual would cause in a population that is fully susceptible. This threshold parameter is highly valuable in characterizing mathematical problems related to infectious diseases. If R0 < 1, this suggests that, on average, during the infectious period, an infected individual produces less than one new infected individual, suggesting that the infection may eventually be eradicated from the population. On the other hand, if R0 < 1, every infected person develops an average of multiple new infections, it suggests that the disease may continue to spread throughout the population. We discuss the Reproduction number in this work and provide some examples, both for straightforward and complicated situations.
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    Population dynamics of a mathematical model for Campylobacteriosis
    (Proceedings of International Conference on Mathematical Modelling Optimization and Analysis of Disease Dynamics (ICMMOADD), 2024-02-22) Ashezua, T. T.; Salemkaan, M. T.; Somma, Samuel Abu
    The bacterium campylobacter is the cause of campylobacteriosis, a major cause of foodborne illness that goes by the most common name for diarrheal illnesses. This paper develops and analyzes a new mathematical model for campylobacteriosis. It is demonstrated that in cases where the corresponding reproduction number is smaller than unity, the model's disease-free equilibrium is both locally and globally stable. The numerical simulation results indicate that increasing the treatment rate for both symptomatic and asymptomatic disease-infected individuals resulted in a decrease in the number of asymptomatic and symptomatic individuals, respectively, and a rise in the population's number of recovered individuals.