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Pandemic bounds for an epidemic on an infinite lattice. (English) Zbl 1065.92049
Summary: Exact results have previously been obtained concerning the spread of infection in continuous space contact models describing a class of multi-type epidemics. Pandemic lower and upper bounds were obtained for the spatial final size. Pandemic results have also been obtained for a discrete space model on the integer lattice using an infinite matrix formulation of the final size equations. However, the proof required restrictive constraints to be placed on the model parameters which do not hold in general and will not be valid when infection modifies behaviour. The purpose of this paper is to remove these constraints and give a general proof of the pandemic results for the multi-type epidemic on the lattice $$Z^N$$.

MSC:
 92D30 Epidemiology 15A99 Basic linear algebra 60K35 Interacting random processes; statistical mechanics type models; percolation theory
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