School of Physical Sciences (SPS)
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School of Physical Sciences (SPS)
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Item Modelling the Impacts of Media Campaign and Double Dose Vaccination in Controlling COVID-19 in Nigeria(Alexandria Engineering Journal, 2023-01-15) Akinwande, N. I.; Somma, Samuel Abu; Olayiwola, R. O.; Ashezua, T. T.; Gweryina, R. I.; Oguntolu, F. A.Corona virus disease (COVID-19) is a lethal disease that poses public health challenge in both developed and developing countries of the world. Owing to the recent ongoing clinical use of COVID-19 vaccines and noncompliance to COVID-19 health protocols, this study presents a deterministic model with an optimal control problem for assessing the community-level impact of media campaign and double-dose vaccination on the transmission and control of COVID-19. Detailed analysis of the model shows that, using the Lyapunov function theory and the theory of centre manifold, the dynamics of the model is determined essentially by the control reproduction number (𝑅𝑚𝑣). Consequently, the model undergoes the phenomenon of forward bifurcation in the absence of the double dose vaccination effects, where the global disease-free equilibrium is obtained whenever 𝑅𝑚𝑣 ≤ 1. Numerical simulations of the model using data relevant to the transmission dynamics of the disease in Nigeria, show that, certain values of the basic reproduction number ((𝑅0 ≥ 7)) may not prevent the spread of the pandemic even if 100% media compliance is achieved. Nevertheless, with assumed 75% (at 𝑅0 = 4)) media efficacy of double dose vaccination, the community herd immunity to the disease can be attained. Furthermore, Pontryagin’s maximum principle was used for the analysis of the optimized model by which necessary conditions for optimal controls were obtained. In addition, the optimal simulation results reveal that, for situations where the cost of implementing the controls (media campaign and double dose vaccination) considered in this study is low, allocating resources to media campaign-only strategy is more effective than allocating them to a firstdose vaccination strategy. More so, as expected, the combined media campaign-double dose vaccination strategy yields a higher population-level impact than the media campaign-only strategy, double-dose vaccination strategy or media campaign-first dose vaccination strategy.Item A Global Asymptotic Stability of COVID-19 Diabetes Complication Free Equilibrium(Journal of Science, Technology, Mathematics and Education (JOSTMED), 2024-03-25) Yusuf, A,; Akinwande, N. I.; Olayiwola, R. O.; Kuta, F. A.; Somma, Samuel AbuIn this paper, a Mathematical modelling of COVID-19 incorporating the comorbidity of Diabetes was established base on the accompanying assumptions, a global asymptotic of the same model was developed by applying the theorem of Castillo-Chavez by fixing a point to be globally asymptotic stable equilibrium of the system, provided that and the two set conditions are satisfied. It is very clear that so the conditions are not met. Hence, may not be globally asymptotically stable when .Item 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].Item Stability Analysis of a Mathematical Modeling of Spread and Control of Corona Virus Disease (Covid-19) Incorporating Vaccination Class(Journal of Balkan Science and Technology, 2023-04-30) Chembe, J; Somma, Samuel AbuIn this paper some mathematical models of COVID 19 were extended by incorporating vaccination, social distancing, and proper use of face mask and hand sanitizers for the spread and control of Corona virus (COVID-19). The analysis of the Disease-Free Equilibrium (DFE) and Endemic Equilibrium (EE) points were carried out. The trace -determinant approaches for local stability and Castilo-chaves for global stability were used in the stability and sensitivity analyses. At the stability of the equilibrium points, we find out that the basic reproduction number which implies the (DFE) is locally asymptotically stable, but global asymptotic stability of (EE) exists at . Sensitivity analysis identifies the model's most sensitive parameters; which are responsible for disease transmission and control. Visualization of the effect of the key parameters on the basic reproduction number was carried out. The data visualization demonstrates that vaccination and recovery rate are crucial parameters for eradicating COVID-19 from the population, while contact rate, lack of social distancing, and improper use of facemasks and hand sanitizers are crucial for COVID-19 persistence. The risks of close proximity to infected people should indeed be made known to the general public. The government needs to step up its vaccination efforts.