Epidemic Modelling: An Introduction (Cambridge Studies in Mathematical Biology, Series Number 15)

This book tells what we knew about the mathematics of epidemics up until 1990. The differential equations (beginning with Bernoulli and moving forward) are presented well. That is, the variables are defined in the text and not too many steps are skipped in the derivations. The high point in this type of epidemiology came in 1927, when Kermack and McKendrick wrote the continuous-time epidemic equations. Diseases were characterized by the parameter rho, the relative removal rate. Up until the 1990s, we were just fitting our data to this model, and estimating rho. Along came 'computational biology', or 'agent-based models' or 'numerical methods'. After 1990, these new techniques allowed us to escape from the perfect-mixing assumption that caused the Kermack and McKendrick model to depart from reality. With computation, we were able to see the impact of social networks, targeted innoculuations, and to test the value of different intervention strategies. See March 2005 Scientific American. None of those advances are discussed in this book. As a historical treatise, however, it is a superb addition to the library. This general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics

This general introduction to the mathematical techniques needed to understand epidemiology begins with an historical outline of some disease statistics dating from Daniel Bernoulli's smallpox data of 1760. The authors then go on to describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (nonhomogeneous) populations. They offer a range of methods for constructing and analyzing models, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumors and macro-parasitic diseases. Questions of fitting data to models, and the use of models to understand methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text.

This general introduction to the ideas and techniques required for the mathematical modeling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (nonhomogeneous) populations. Several techniques for constructing and analyzing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumors and vector-borne diseases such as malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. This is a general introduction to the mathematical techniques needed to understand epidemiology. It begins with an historical outline of some disease statistics, before describing simple deterministic and stochastic models The mathematical study of diseases and their dissemination is at most just over three centuries old.