Faculty of Physical Sciences

Mathematical Modeling Relating Psychosocial Therapy as a Veritable Panacea for Bipolar Ii Disorder Patient

2019-11-01T00:00:00Z

Mathematical Modeling Relating Psychosocial Therapy as a Veritable Panacea for Bipolar Ii Disorder Patient Michael, Uchenna Emmanuel This study applies mathematical models to emotional variation in patients with bipolar II disorder using dynamical oscillator. Three models of the mood swing are studied and solved using multiple scale perturbation and some numerical simulation. We first incorporated the psychosocial therapy in the forcing function which reveals that if Family and Friends Therapy (FFT) is constructively administered the patient recuperate speedily. The second model studies the effect of HPA axis secretions to the emotional variation of bipolar II disorder patient; it is observed that the increase or decrease of the HPA hormone from the basal level in the body system affects the mood variation of bipolar II disorder patients but should not be used as an etiology maker. Finally, Fractional – ordered oscillator is used to model the mood variation of bipolar II disorder patient to absorb the continuous stressors in the environment that triggers the illness; it is observed that the fractional model brings out a better explaination of the medication parameter (pharmacotherapy and psychotherapy) effect on the amplitude (magnitude) of the mood of the patient with the stressors variation. Generally, it is observed that FFT is of great importance for the recuperation of the patient when combined with administered psychotic drugs both for in the onset of the disorder and the diagnosed patient.

Mathematical Model on Middle East Respiratory Syndrome and Control

2019-11-01T00:00:00Z

Mathematical Model on Middle East Respiratory Syndrome and Control Ezema, Godwin Izuchukwu In this work,we considered the general overview of Middle East Respiratory Syndrome(MERS-CoV). A model for the transmission dynamics of the disease infection with control was formulated using a set of ordinary differential equations. The solution to the model equations were obtained using Homotopy Perturbation method, and ways for controlling or preventing the disease presented. The effective reproduction number ,R0 of the system was obtained and it was shown that the disease will spread only if R0 > 1 and would die off with time, if R0 < 1. Numerical simulations carried out on the model showed that with the judicious use of Modified Virus Ankara(MVA) in combination with MERS-CoV inoculation, the disease will phase out rapidly in the population.

A Fractional Mathematical Model on Transmission and Control of the Spread of Myiasis in Human System Using Insect Repellents

2019-11-01T00:00:00Z

A Fractional Mathematical Model on Transmission and Control of the Spread of Myiasis in Human System Using Insect Repellents Eze, Hyginus Ejike In this project, we proposed a fractional Susceptible, Expose, Infected, Treated and Recovered order model to study the transmission dynamics of Myiasis. We showed the existence of the equilibrium states. The basic reproduction number of the model was evaluated in terms of parameters in the model using the next generation matrix approach. We provided the conditions for the stability of the diseasefree and the endemic equilibrium points. A detailed stability analysis of the model was carried out. Numerical simulations of the model were carried out using Adams-type predictor-corrector method which showed in detail the population dynamics of the disease. From the simulations, the level of impacts of the parameters of the model were demonstrated.

Analysis of a Fractional Order Model for Influenza A

2018-08-01T00:00:00Z

Analysis of a Fractional Order Model for Influenza A Nwachukwu, Anthonia Uchenna In this project work, a fractional order mathematical model that describe the transmission dynamics of Influenza A Virus was given and control mechanism for the spread of the Virus was given. Qualitative dynamics of the model is determined by the basic reproduction number,R_0 using the next generation matrix. Through the analysis of the model, the stability conditions of the equilibria were derived using Jacobian transformation method. To illustrate our theoretical analysis, some numerical simulations were carried out using Adams-type predictor-corrector method to show the behavior of the solutions of the proposed fractional order system. The simulation results provide a theoretical basis to control the spread of influenza A and also show that the fractional model is better than the classical model.