Abstract
Connections exist between n-type contact branching processes and deterministic models for spatial epidemics. Let the position of the furthest individual in a contact branching process from position 0 at time t in a given direction be denoted by U(t). Define \(y_i(s,t) = P[U(t) > s| \ \textup{one} \ \textup{type} \ i \ \textup<Subscript>dividual</Subscript> \ \textup{at} \ \textup{position} \ 0 \ \textup{at} \ \textup{time} \ t = 0]\). This paper discusses how the methodology developed for considering the asymptotic speed of propagation of infection in n-type spatial epidemics can be modified to look at the behaviour of y i(s,t). This leads in certain cases to a proof of the result that U(t)/t converges in probability to c 0, the minimum speed for which wave solutions exist in a particular system of equations. The application of an approximate saddle point method to more general contact branching processes is also discussed.
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Radcliffe, J., Rass, L. (1995). Multitype Contact Branching Processes. In: Heyde, C.C. (eds) Branching Processes. Lecture Notes in Statistics, vol 99. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2558-4_17
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DOI: https://doi.org/10.1007/978-1-4612-2558-4_17
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