Mathematics
Permanent URI for this collectionhttp://197.211.34.35:4000/handle/123456789/200
Mathematics
Browse
11 results
Search Results
Item SENSITIVITY ANALYSIS FOR THE MATHEMATICAL MODELLING OF MONKEY POX VIRUS INCORPORATING QUARANTINE AND PUBLIC ENLIGHTENMENT CAMPAIGN(FULafia Journal of Science & Technology, 2020-03-15) Somma, Samuel AbuIn this paper sensitivity analysis was carried out for the mathematical modeling of Monkey pox virus incorporating quarantine and public enlightenment campaign into the human population. The model was formulated using first order ordinary differential equations. The model equation was divided into two populations of human and rodents. There are two equilibrium points that exist in the model; Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The Local and Global stabilities of Disease Free Equilibrium (DFE) were R and rodent to rodent analyzed. The basic reproduction numbers of human to human 0h r R0 transmission was computed. The sensitivity analysis of the Basic reproduction number with the parameters was carried out. The Disease Free Equilibrium (DFE) is Locally and Globally Asymptotically Stable if R 0 h < 1 and R 0 r < 1 . The graphical presentation of the Basic reproduction number and the sensitive parameters shows that effective progression rate from infected class to Quarantine and effective public enlightenment campaign are the most sensitive parameters that will eradicate the disease from the population.Item Homotopy Perturbation Method (HPM) for Solving Mathematical Modeling of MonkeyPox Virus(National Mathematical Centre (NMC) Journal of Mathematical Sciences, 2020-03-03) Somma, Samuel Abu; Ayegbusi, F. D.; Gana, P.; Adama, P. W.; Abdurrahman, N. O.; Eguda, F. Y.Mathematical modeling of real life problems such as transmission dynamics of infectious diseases resulted into non-linear differential equations which make it difficult to solve and have exact solution. Consequently, semi-analytical and numerical methods are used to solve these model equations. In this paper we used Homotopy Perturbation Method (HPM) to solve the mathematical modeling of Monkeypox virus. The solutions of HPM were validated numerically with the Runge-Kutta-Fehlberg 4-5th order built-in in Maple software. It was observed that the two solutions were in agreement with each other.Item Application of Adomian Decomposition Method (ADM) for Solving Mathematical Model of Measles(National Mathematical Centre (NMC) Journal of Mathematical Sciences,, 2021-03-03) Somma, Samuel Abu; Ayegbusi, F. D.; Gana, P.; Adama, P. W.; Abdurrahman, N. O.; Eguda F. Y.Adomian Decomposition Method (ADM) is a semi-analytical method that give the approximate solution of the linear and non-linear differential equations. In this paper the Adomian Decomposition Method (ADM) was used to solve the mathematical model of measles. The ADM solution was validated with Runge-Kutta built-in in Maple software. The graphical solutions show the decrease and increase in the classes with time. It was revealed from the graphical solution that the ADM is in agreement with Runge-Kutta. Keywords: Mathematical modeling, Adomian Decomposition Method, numerical solutionItem MODELLING FIRE SPREAD REACTION RATE IN ATMOSPHERIC WEATHER CONDITION(Science World Journal, 2021-05-12) Zhiri, A. B.,; Olayiwola, R.O.; Somma, Samuel Abu; Oguntolu, F. A.Fire spread in any fire environment is a thing of great concern as wind is arguably the most important weather factor that influences the spread of fire. In this paper, we present equations governing the phenomenon and assume the fire depends on the space variablex. Analytical solution is obtained via perturbation method, direct integration and eigenfunction expansion technique, which depicts the influence of parameters involved in the system. The effect of change in parameters such as Peclet mass number and Equilibrium wind velocity are presented graphically and discussed. The results obtained revealed that both Peclet mass number and Equilibrium wind velocity enhanced oxygen concentration during fire spread.Item APPROXIMATE SOLUTIONS FOR MATHEMATICAL MODELLING OF MONKEY POX VIRUS INCORPORATING QUARANTINE CLASS(Transactions of the Nigerian Association of Mathematical Physics, 2021-03-30) Somma, Samuel Abu; Akinwande, N. I.,; Ashezua, T. T.; Nyor, N.; Jimoh, O. R.; Zhiri, A. B.In this paper we used Homotopy Perturbation Method (HPM) and Adomian Decomposition Method (ADM) to solve the mathematical modeling of Monkeypox virus. The solutions of HPM and (ADM) obtained were validated numerically with the Runge-Kutta-Fehlberg 4-5th order built-in in Maple software. The solutions were also presented graphically to give more insight into the dynamics of the monkeypox virus. It was observed that the two solutions were in agreement with each other and also with Runge-Kutta.Item SEMI-ANALYTIC METHODS FOR THE SOLUTION OF TWO EPIDEMIOLOGICAL MODELS(Transactions of the Nigerian Association of Mathematical Physics, 2021-12-02) Enoch, B. T.; Ashezua, T, T.; Somma, Samuel AbuIn this paper, we apply three semi-analytical methods, viz: the Differential Transform Method (DTM), Homotopy Perturbation Method (HPM) and the Variational Iteration Method (VIM) to compute approximate solutions of a continuous mathematical model of Shigella diarrhea comprising of a non-constant population and a deterministic model on the impact of stress on the dynamics and treatment of Tuberculosis.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; bifurcationItem A Mathematical Model for Water Quality Assessment: Evidence-Based from Selected Boreholes in Federal University Dutse, Nigeria(UMYU Scientifica, 2023-12-30) Eguda, F. Y.; Amoo, A. O.; Adamu, S. B.; Ogwumu, O. D.; Somma, Samuel Abu; Babura I. B.The present study assessed the quality of water sampled from different boreholes on the campus of Federal University Dutse, Nigeria, using a mathematical modelling approach. A model for estimating water quality was developed based on physicochemical parameters such as pH, electrical conductivity, temperature, turbidity, and total hardness measured from each borehole. The correlation analysis of physicochemical data indicates a strong correlation of about 99% between the real-life data collected from six (6) different boreholes and the model’s predictions. From the results, the sensitivity analysis revealed that electrical conductivity plays the highest role in determining water quality, followed by total hardness, temperature has the third highest impact, followed by turbidity, the fourth, and pH has the least impact in determining water quality in the listed boreholes. Therefore, in any case of intervention, the water quality regulatory body should be sent regularly to the tertiary institutions in the state for routine check-ups.Item COA-SOWUNMI'S LEMMA AND ITS APPLICATION TO THE STABILITY ANALYSIS OF EQUILIBRIUM STATES OF THE NON-LINEAR AGE-STRUCTURED POPULATION MODEL(International Journal of Mathematics and Physical Sciences Research, 0205-04-10) Akinwande, N. I.; Somma, Samuel AbuAbstract: In this work, we present a result in the form of a lemma which we name COA-Sowunmi’s Lemma, its proof and application to the stability analysis of the transcendental characteristics equation arising from the perturbation of the steady state of the non-linear age-structured population model of Gurtin and MacCamy [11]. Necessary condition for the asymptotic stability of the equilibrium state of the model is obtained in the form of constrained inequality on the vital parameters of the model. The result obtained is then compared with that of an earlier work by the [4].