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Applied Mathematics Commons™

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Mathematics

Olusegun Michael Otunuga

Selected Works

Articles 1 - 6 of 6

Full-Text Articles in Applied Mathematics

Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model.Pdf, Michael Otunuga Sep 2019

Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model.Pdf, Michael Otunuga

Olusegun Michael Otunuga

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to …

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Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga Feb 2019

Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga

Olusegun Michael Otunuga

This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary …

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Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications.Pdf, Olusegun M. Otunuga Jan 2019

Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications.Pdf, Olusegun M. Otunuga

Olusegun Michael Otunuga

In this work, an attempt is made to apply the Local Lagged Adapted Generalized Method of Moments (LLGMM) to estimate state and parameters in stochastic differential dynamic models. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and non-stationary stochastic dynamic model validation problems in biological, chemical, engineering, energy commodity markets, financial, medical, physical and social sciences. The byproducts of this innovative approach (LLGMM) are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic process (DTIDMLSMVSP). …

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Global Stability For A 2n+1 Dimensional Hiv Aids Epidemic Model With Treatments, Olusegun M. Otunuga Mar 2018

Global Stability For A 2n+1 Dimensional Hiv Aids Epidemic Model With Treatments, Olusegun M. Otunuga

Olusegun Michael Otunuga

In this work, we derive and analyze a 2n+1-dimensional deterministic differential equation modeling the transmission and treatment of HIV (Human Immunodeficiency Virus) disease. The model is extended to a stochastic differential equation by introducing noise in the transmission rate of the disease. A theoretical treatment strategy of regular HIV testing and immediate treatment with Antiretroviral Therapy (ART) is investigated in the presence and absence of noise. By defining $R_{0,n}$, $R_{t,n}$ and $\mathcal{R}_{t,n}$ as the deterministic basic reproduction number in the absence of ART treatments, deterministic basic reproduction number in the presence of ART treatments and stochastic reproduction number …

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Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation.Pdf, Michael Otunuga Aug 2017

Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation.Pdf, Michael Otunuga

Olusegun Michael Otunuga

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In this work, an attempt is made to estimate time varying parameters in a linear stochastic differential equation. By defining $m_{k}$ as the local admissible sample/data observation size at time $t_{k}$, parameters and state at time $t_{k}$ are estimated using past data on interval $[t_{k-m_{k}+1}, t_{k}]$. We show that the parameter estimates at each time $t_{k}$ converge in probability to the true value of the parameters being estimated. A numerical simulation is presented by applying the local lagged adapted generalized method of moments (LLGMM) method to the stochastic differential models governing prices …

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Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun M. Otunuga Jan 2017

Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun M. Otunuga

Olusegun Michael Otunuga

We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic ($R_{0}$) and stochastic ($\mathcal{R}_{0}$) basic reproductive number. Contrary to some author's remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (that is, $R_{0}<1$), epidemic can still …

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