Mathematics
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Mathematics
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Item Stability Analysis of the Mathematical Modelling of Transmission and Control of Rabies Incorporating Vaccination Class(Dutse Journal of Pure and Applied Sciences (DUJOPAS),, 2022-03-12) Abdurrahman, Nurat Olamide; Somma, S. A.; Balogun R. T.; Eguda F. Y.; Adama, P. W.; Yisa E. M.Rabies is a viral disease of the nervous system that is often transmitted to human beings through the bite or scratch of rabid animals. The uprising of insecurity globally has forced several people to get dogs into their homes. This paper formulated the mathematical model of rabies transmission and control by incorporating vaccination class. The model's Disease Free Equilibrium (DFE) state was obtained and used to compute the basic reproduction number R0. Local stability analysis of the DFE was carried out using Jacobian Matrix techniques. The DFE is locally asymptotically stable if R0 < 1.Item Mathematical Modeling of the Spread of False Information within Social Media(Ilorin Journal of Science, 2024-10-15) Abdurrahman, Nurat Olamide; Ibrahim, M. O.; Ibrahim, J. O.One of the societal pollutions in our environment that requires overhauling intervention is the spread of false information. In this paper, we modelled the spread of rumor in a continuous and dynamic population of five compartments. We considered an incubation period which allows rumormongers to verify the authenticity of information received before spreading. Stability analysis of the rumor-free equilibrium (RFE) and the rumor-present equilibrium (RPE) was carried out. The RPE is a function of the reproduction number R0. In order to annihilate the rumor, the results suggest that we should reduce R0 continuously below 1. The results are numerically validated and discussed.Item Stability Analysis of the Mathematical Modelling of Transmission and Control of Rabies Incorporating Vaccination Class(Dutse Journal of Pure and Applied Sciences (DUJOPAS), 2022-03-02) Somma, Samuel Abu; Balogun, R. T.; Eguda, F. Y.; Abdurrahman, N. O.; Adama, P. W.; Yisa E. M.Rabies is a viral disease of nervous system that is often transmitted to human beings through the bite or scratch of rabid animals. The uprising of in-security globally has forced several people to get dogs in their houses. In this paper the mathematical model of rabies transmission and control was formulated by incorporating vaccination class. The Disease Free Equilibrium (DFE) state of the model was obtain and used to compute the basic reproduction number 0 R . Local stability analysis of the DFE was carried out using Jacobian Matrix techniques. The DFE is locally asymptotically stable ifItem Modelling and analysis of a model for Chlamydia Trachomatis transmission dynamics(International Journal of Mathematical Analysis and Modelling, 2023-11-20) Ashezua, T. T.; Ibekwe, J. J.; Somma, Samuel AbuChlamydia infection, one of the commonest sexually transmitted infections (STIs), remain a public health challenge in both underdeveloped and developed countries of the world. Chlamydia trachomatis has been observed to have negative health consequences hence much research work is needed to be done to curb the spread of the disease in the population. In this paper, a mathematical model for studying the impact of condom usage and treatment on the transmission dynamics and control of Chlamydia in the population is presented. Qualitative analysis of the model shows that it undergoes the phenomenon of backward bifurcation. In the absence of this phenomenon (which is showntooccurasaresult of the reinfection of recovered individuals), the disease-free equilibrium of the modelis globally asymptotically stable whenever the associated reproduction number is less than unity. Further, for the same scenario as above, it is shown that the unique endemic equilibrium of the model exists whenever the reproduction number is greater than unity. Numerical results show a relationship between the progression rate, treatment rate and the reproduction number. Results from the sensitivity analysis of the model, using the reproduction number, Rc reveal that the top parameters that significantly drive the dynamics of Chlamydia in the population are the efficacy of condoms, condom compliance, a fraction of treated individuals who recover due to effective treatment and treatment rate. Numerical simulations of the model suggest that infected persons after treatment should wait for at least 7 days before engaging in any form of sexual activity or, if not possible use condoms correctly (to avoid reinfection) in order to effectively control the spread of the disease in the population. Keywords:Chlamydia; reproduction number; reinfection; stability; bifurcation