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

Individual based SIR model (page 269)

Individual-based models can encompass a wide range of model forms, and can be designed to include a variety of complex and detailed host behavior that could not be readily expressed within the other model types. As the name suggests, these models consider the dynamics of individuals that occupy a spatial landscape. Here, as an example of this methodology, we formulate a general stochastic individual-based model based on the simple SIR model in which only two events are possible: recovery which occurs at rate γ for any infected individual and transmission which is a spatial process. The rate of transmission (or force of infection) to a susceptible individual, i, is given by:

where the sum is over all infectious individuals (labelled j), dij is the distance between individuals i and j, and KT is the transmission kernel. In these programs the kernel is a power-law decay: KT(d) = d

is the length of the 2-D square in which simulations take place.
is the population size, randomly distributed in 2-D
is the transmission rate which scale the spatial kernel
is the power-law decay associated with the spatial kernel.
γ is called the removal or recovery rate.
is the number of initially infected individuals
All rates are specified in days.

All parameters must be positive.


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