Modeling Infectious Diseases in Humans and Animals
Matt J. Keeling & Pejman Rohani

Multi-Pathogen/Multi-Host Models

Chapter 4 is dedicated to two main issues: heterogeneties of the pathogen and heterogeneties of the host. Pathogen heterogeneities concentrates on modelling the interaction between competing strains of infection. The scientific community is only just beginning to understand the range of complex outcomes when multiple strains compete for a limited supply of susceptibles. This conceptual extension of the simple one-pathogen one-host paradigm are becoming increasingly recognized as fundamental to our understanding of key questions in public health. A complete description of models that examine strain dynamics requires a detailed knowledge of the host immune systems, and how different strains interact via the immune response that they elicit. Interest in this area stems from the fact that competition between strains is fundamental to disease evolution. Thus, if we are to understand and ultimately predict the emergence of novel pathogens or, for example, the strain of influenza that will circulate next season, we must better grasp the role of competition between cross-reacting strains of infection.We develop a series of ever-more complex models to explore the interaction between two or more pathogens (Programs 4.1-4.3).
Finally, we consider the problem of two hosts that share a common pathogen, and focus in particular on the dynamics of infection spread by mosquito vectors. Vector-borne diseases, such as malaria, dengue fever, and leishmania, are among the most challenging from a public-health perspective, and so models are frequently required to optimize their control.

Program 4.1
Page 118
SIR model with partial immunity
Program 4.2
Page 123
Partial immunity model that cycles
Program 4.3
Page 126
Full partial immunity model
Program 4.4
Page 136
SIR model for mosquito vectors

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Matt Keeling      Pejman Rohani