Bulletin of Mathematical Biology

, 66:91

First online:

The effects of spatial movement and group interactions on disease dynamics of social animals

  • I. GudeljAffiliated withBiomathematics Unit, Rothamsted Research Email author 
  • , K. A. J. WhiteAffiliated withDepartment of Mathematics, University of Bath
  • , N. F. BrittonAffiliated withDepartment of Mathematics, University of Bath

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The effects of spatial movements of infected and susceptible individuals on disease dynamics is not well understood. Empirical studies on the spatial spread of disease and behaviour of infected individuals are few and theoretical studies may be useful to explore different scenarios. Hence due to lack of detail in empirical studies, theoretical models have become necessary tools in investigating the disease influence in host-pathogen systems.

In this paper we developed and analysed a spatially explicit model of two interacting social groups of animals of the same species. We investigated how the movement scenarios of susceptible and infected individuals together with the between-group contact parameter affect the survival rate of susceptible individuals in each group. This work can easily be applied to various host-pathogen systems.

We define bounds on the number of susceptibles which avoid infection once the disease has died out as a function of the initial conditions and other model parameters. For example, once disease has passed through the populations, a larger diffusion coefficient for each group can result in higher population levels when there is no between-group interaction but in lower levels when there is between-group interaction. Numerical simulations are used to demonstrate these bounds and behaviours and to describe the different outcomes in ecological terms.