Divine Wanduku - Academia.edu (original) (raw)

Papers by Divine Wanduku

Presentation given at the Southern Georgia Mathematics Conference. Abstract Booklet According to ... more Presentation given at the Southern Georgia Mathematics Conference. Abstract Booklet According to the WHO, globally, as of March 5, 2021, Coronavirus Disease 2019 (COVID-19) has infected over 115 million people, caused over 2.5 million deaths and widespread economic downturn. In this talk, we present our modeling, numerical simulation, and analysis of the stochastic dynamics of COVID-19 in a closed population that is considered the starting point of the outbreak of the disease. We present two COVID-19 epidemic models for the population, where at any given time an individual can be in any of the following categories: susceptible, exposed and mildly infectious, asymptomatic and infectious, symptomatic and infectious, symptomatic hospitalized and infectious, recovered with partial immunity, or deceased from disease related causes. Both models are discrete-time Markov chain (DTMC) models with multinomial transition probabilities. Using CDC data on daily infection rate for the state of Ge...

Presentation given as part of Celebrating Dr. Ngwa\u27s 55th birthday with talks honoring his mat... more Presentation given as part of Celebrating Dr. Ngwa\u27s 55th birthday with talks honoring his mathematical modeling work including malaria mosquitoes Mathematical Epidemiology Subgroup (MEPI), SMB 2021

Presentation given at the Southern Georgia Mathematics Conference. Abstract Booklet A novel discr... more Presentation given at the Southern Georgia Mathematics Conference. Abstract Booklet A novel discrete time general Markov chain SEIRS epidemic model with vaccination is derived and studied. The model incorporates finite delay times for disease incubation, natural and artificial immunity periods, and the period of infectiousness of infected individuals. The novel platform for representing the different states of the disease in the population utilizes two discrete time measures for the current time of a person’s state, and how long a person has been in the current state. Two sub-models are derived based on whether the drive to get vaccinated is inspired by close contacts with infectious individuals or otherwise. Sensitivity analysis is conducted on the two models to determine how vaccination affects disease eradication

Presented at Joint Statistics Seminar, Joint Mathematics and Statistics Colloquiums, in MP 3314, ... more Presented at Joint Statistics Seminar, Joint Mathematics and Statistics Colloquiums, in MP 3314, Department of Mathematical Sciences, Georgia Southern University Recently, traditional epidemic models are increasingly used to investigate social infectious disease systems such as the spread of rumors and toxic ideas in an online social media networks such as Facebook, Twitter and Microblog etc. Rumors can affect our emotional and physical lives in the same manner as other types of infectious diseases. In this new area of application, random graph theoretical models, stochastic models, statistical models, and differential equation models are used to represent and analyze the dynamic spread of rumors and control. In this study, using some ideas from graph theory and stochastic processes, we present a Markov chain model for the stochastic spread of a malicious rumor. The model consists of spreaders (I) who post malicious messages on websites. The ignorant (S) are infected and become exposed (E) to the malicious rumor after reading the posts. Some exposed who are eager to spread the messages on other susceptible websites are labelled “weakly exposed”. Other exposed people who have change of mind, and are reluctant to spread the messages are labelled “strongly exposed”. The “weakly exposed” become spreaders, and the “strongly exposed” become stiflers (R). We show how to derive the model on a complex heterogeneous social random network, and find transition probabilities. We also use statistical methods to estimate vital parameters of the model such as the probability of getting infected by a terrorist on the online social network. We present numerical examples and figures to show how the malicious rumor evolves in the online social network over time

Presented at Georgia Southern University Student Research Symposium 2019 Prof. Divine Wanduku men... more Presented at Georgia Southern University Student Research Symposium 2019 Prof. Divine Wanduku mentored student, Chinmoy Rahul

Presented at Georgia Southern University Student Research Symposium 2019. Prof. Divine Wanduku me... more Presented at Georgia Southern University Student Research Symposium 2019. Prof. Divine Wanduku mentored Omotomilola Jegede

We propose a new generalized family of distributions called the exponentiated generalized power s... more We propose a new generalized family of distributions called the exponentiated generalized power series (EGPS) family of distributions and study its sub-model, the exponentiated generalized logarithmic (EGL) class of distributions, in detail. The structural properties of the new model (EGPS) and its sub-model (EGL) distribution including moments, order statistics, Rényi entropy, and maximum likelihood estimates are derived. We used the method of maximum likelihood to estimate the parameters of this new family of distributions. Simulation study was carried out to examine the bias and the mean square error of the maximum likelihood estimators for each of the model\u27s parameters. Finally, we showed real life data examples to illustrate the models\u27 applicability, flexibility and usefulness

Cornell University - arXiv, Jul 24, 2019

We present a class of SEIR Markov chain models for infectious diseases observed over discrete tim... more We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions between states of the population. The SEIR models consist of random dynamical equations for each state (S, E, I and R) involving driving events for the process. We characterize some special types of SEIR Markov chain models in the class including: (1) when birth and death are zero or non-zero, and (2) when the incubation and infectious periods are constant or random. A detailed parameter estimation applying the maximum likelihood estimation technique and expectation maximization algorithm are presented for this study. Numerical simulation results are given to validate the epidemic models.

Virtual presentation given at 2020 SIAM Conference on the Life Sciences Deriving a robust statist... more Virtual presentation given at 2020 SIAM Conference on the Life Sciences Deriving a robust statistical scheme to approximate important epidemiological control parameters such as the basic reproduction number (BRN), the probability of no spread of a disease etc. is a very important first step in determining the prognosis of diseases. In this talk, a discrete time Markov chain (DTMC) model for influenza epidemics with vaccination and removed states is derived and studied in a novel framework, where the various compartments of the infectious and vaccinated states of the system are generated over the infectious and immunity periods. The DTMC model consists of trinomial transition probabilities, and they are also derived under special assumptions of correlated vaccination and infection probabilities at any instant. The techniques of maximum likelihood estimation (MLE), and expectation maximization (EM) algorithm are applied to find estimates for the SVIR model parameters and the BRN. The ...

In this paper the almost sure exponential convergence and pth mean exponential convergence of a g... more In this paper the almost sure exponential convergence and pth mean exponential convergence of a general nonlinear stochastic epidemic model are investigated. The stochastic epidemic model consists of Ito-stochastic differential equations with multiple-delays and general nonlinear incidence rate. The stochastic convergence and exponential stabilities of the epidemic model are examined and applied to find control measures for the disease. Moreover, the basic reproduction number for the disease is computed

Presentation given at Biology and Medicine Through Mathematics Conference (BAMM). Conference was ... more Presentation given at Biology and Medicine Through Mathematics Conference (BAMM). Conference was originally scheduled for May 2020 but was rescheduled to May 2021 due to the covid-19 pandemic

Presentation given at Graduate Student Seminar Prof. Divine Wanduku mentored Cameron Newma

We introduce a new distribution called the Gamma Log-logistic Erlang Truncated Exponential (GLLoG... more We introduce a new distribution called the Gamma Log-logistic Erlang Truncated Exponential (GLLoGETE) distribution. Structural properties of the distribution including series expansion of the density function, sub-models, hazard function, moments, conditional moments, mean deviations, distribution of order statistics, Renyi entropy and maximum likelihood estimates are presented. The ´ new pdf is an infinite linear combinations of Burr XII-Erlang Truncated Exponential distributions. The new generalized distribution is applied to real data sets to evaluate the model performance

Presented at Disease Dynamics Seminars, College of Public Health, Georgia Southern University Lin... more Presented at Disease Dynamics Seminars, College of Public Health, Georgia Southern University Link to Program: https://sites.google.com/a/georgiasouthern.edu/fung/disease-dynamics-seminars A stochastic epidemic dynamic model for vector-borne diseases in network structured populations involving two hierarchic levels (two-scales) is presented. Infected persons change state from Susceptible to Infectious and then to Removal, and back to Susceptible (SIRS). The delay in the epidemic dynamic process owing to the incubation the disease is incorporated into the dynamic system as a random process. Furthermore, the disease dynamics presented is influenced by fluctuations in the disease transmission process as well as the two-scale human mobility process. The threshold conditions for disease eradication at three human-vector contact levels in the two-scale population are computed, and the results for the long -term (asymptotic) stochastic stability of the steady states (equilibria) of the system derived are presented. Moreover the asymptotic stability results are exhibited in several real life scenarios and the significance of the results are presented. Numerical simulation results are presented

An interesting topic for investigation in the study of stochastic differential equation epidemic ... more An interesting topic for investigation in the study of stochastic differential equation epidemic models involving Brownian motion perturbations concerns the permanence of disease and existence of a stationary behavior for the state of the stochastic process over time. Conditions for the permanence of the disease hold the key to understand the endemic behavior of the disease; a stationary distribution leads to knowing the statistical properties of the disease over long time. This talk discusses a class of Ito stochastic differential equation SEIRS epidemic models for vector-borne diseases e.g. malaria. Lyapunov functional techniques and some local martingale characterizations are applied to find persistence conditions for the disease by examining the average behavior of all sample paths of the system over time. Moreover, the conditions for the existence of a stationary distribution for the SEIRS system are presented. Furthermore, the stationary distribution is explored numerically.

A Generalized Stochastic SEIRS Epidemic Dynamic Model for Vector-borne Diseases with three Distri... more A Generalized Stochastic SEIRS Epidemic Dynamic Model for Vector-borne Diseases with three Distributed Delays and Nonlinear Incidence. A general stochastic SEIRS triple delay epidemic dynamic model for vector-borne diseases with nonlinear incidence rate is presented. Two of the distributed delays account for the varying incubation period of the infectious agent in the vector and host, and the third distributed delay accounts for the varying immunity period to the disease. Furthermore, the disease dynamics is influenced by random environmental perturbations in the disease transmission and natural death processes. The basic reproduction number-both in the presence and absence of noise are computed. In addition, the stochastic asymptotic properties of the system-asymptotic stability of the equilibria and asymptotic behavior of the system in the neighborhood of equilibria are presented. Moreover the stability results are exhibited in several real life scenarios and the significance of the results are presented. Numerical simulation results are presented.

Cornell University - arXiv, Jul 24, 2019

Presentation given at Graduate Student Seminar Prof. Divine Wanduku mentored Cameron Newma