Bayesian Analysis of Infectious Diseases

COVID-19 and Beyond

Lyle D. Broemeling

• Publisher: Chapman and Hall/CRC
• Year: 2021
• Print ISBN: 9780367633868
• eBook ISBN: 9781000336474
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Bayesian Analysis of Infectious Diseases -COVID-19 and Beyond shows how the Bayesian approach can be used to analyze the evolutionary behavior of infectious diseases, including the coronavirus pandemic. The book describes the foundation of Bayesian statistics while explicating the biology and evolutionary behavior of infectious diseases, including viral and bacterial manifestations of the contagion. The book discusses the application of Markov Chains to contagious diseases, previews data analysis models, the epidemic threshold theorem, and basic properties of the infection process. Also described are the chain binomial model for the evolution of epidemics.

Features:

• Represents the first book on infectious disease from a Bayesian perspective.
• Employs WinBUGS and R to generate observations that follow the course of contagious maladies.
• Includes discussion of the coronavirus pandemic as well as many examples from the past, including the flu epidemic of 1918-1919.
• Compares standard non-Bayesian and Bayesian inferences.
• Offers the R and WinBUGS code on at www.routledge.com/9780367633868

1

Introduction to Bayesian Inferences for Infectious Diseases

1.1Introduction

This book will introduce the reader to the latest Bayesian techniques that analyze the behavior of infectious diseases. A preview of the book is presented, followed by a list of references, and ending with online resources that provide information about emerging infectious diseases and allied subjects.

1.2A Preview of the Book

Chapter 2 describes the foundation of Bayesian statistics. First, Bayesian theorem is given for both discrete and continuous measurements. This necessitates an explanation of the components of Bayes theorem, namely prior information, the posterior distribution of the unknown parameters, and the predictive distribution of future observations. Also provided in this chapter are many examples that illustrate Bayes theorem, among then the standard populations, such as the binomial, the normal, the Poisson, the multivariate normal, and the multinomial, and the Dirichlet.

Chapter 3 explicates the biology and evolutionary behavior of infectious diseases, including viral and bacterial manifestations of the contagion. Next to be explained is that of the immune response via antibodies that attack the invading pathogens. The immune response involves various blood cells (white, red, and platelets) that defend against the disease. Next to be described are drugs that attempt to destroy the components of the disease. A good example of this is quinine and related drugs that control the malaria virus, and drugs that can nearly eradicate the HIV virus of AIDS patients. Although drugs have been very successful in controlling diseases, drug resistance can become a serious issue. This was the case for streptomycin, the breakthrough drug that controlled tuberculosis, but later developed a resistance. Of course, vaccines were a giant advance in medical theory, and one first thinks of the smallpox vaccine against polio. Of course, there are many examples of vaccines, such as those against measles, mumps, and diphtheria. It should be noted that for some viruses, a vaccine is yet to be developed. AIDS and Ebola do not have vaccines, but a very successful treatment for AIDS is successful, but not for Ebola. Of course, transmission of the disease from animals to humans plays an important role in the biology of emerging diseases. It is thought that the coronavirus first appeared in animals (birds, pigs, etc.) in China and was later transmitted to humans in the latter months in 2019. Ebola is believed to have been transmitted by nonhuman African primates to human.

Chapter 4 lays the foundation for Bayesian inference of discrete time Markov chain. The concepts of limiting distributions, transient and recurrent states, ergodic chains, and the period of a chain are defined and explai...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Author
• Chapter 1: Introduction to Bayesian Inferences for Infectious Diseases
• Chapter 2: Bayesian Analysis
• Chapter 3: Infectious Diseases
• Chapter 4: Bayesian Inference for Discrete Markov Chains: Their Relevance to Infectious Diseases
• Chapter 5: Biological Examples Modeled by Discrete Markov Chains
• Chapter 6: Inferences for Markov Chains 
in Continuous Time
• Chapter 7: Bayesian Inference: : Biological Processes that Follow a Continuous Time Markov Chain
• Chapter 8: Additional Information about Infectious Diseases
• Index