Modeling the Stochastic Dynamics of Influenza Epidemics with Vaccination Control, and the Maximum Likelihood Estimation of Model Parameters

This study presents a family of stochastic models for the dynamics of influenza in a closed human population. We consider treatment for the disease in the form of vaccination and incorporate the periods of effectiveness of the vaccine and infectiousness for the individuals in the population. Our model is a SVIR model, with trinomial transition probabilities, where all individuals who recover from the disease acquire permanent natural immunity against the strain of the disease. A special SVIR model in the stochastic family based on correlated vaccination and infection probabilities at any instant is presented. The methods of maximum likelihood and expectation–maximization algorithm are applied to find estimates for the parameters of the chain. Moreover, estimators for some special epidemiological control parameters, such as the basic reproduction number, are computed. A numerical simulation example is presented to find the MLE of the parameters of the model

Modeling Highly Random Dynamical Infectious Systems

Book Summary: This book addresses key aspects of recent developments in applied mathematical analysis and its use. It also highlights a broad range of applications from science, engineering, technology and social perspectives. Each chapter investigates selected research problems and presents a balanced mix of theory, methods and applications for the chosen topics. Special emphasis is placed on presenting basic developments in applied mathematical analysis, and on highlighting the latest advances in this research area. The book is presented in a self-contained manner as far as possible, and includes sufficient references to allow the interested reader to pursue further research in this still-developing field. The primary audience for this book includes graduate students, researchers and educators; however, it will also be useful for general readers with an interest in recent developments in applied mathematical analysis and applications