This paper concerns a probabilistic model of spread of infection on a homogeneous tree. The model is related to stochastic SIR model on graphs. We derive an integral equation for the distribution of the waiting time for an individual to get infected. In a special case the integral equation is equivalent to the Bernoulli differential equation and implies the classic SIR model under an appropriate scaling  .
In this paper we study a discrete probabilistic SIR-type model for the spread of infection on a homogeneous tree. We show that the distribution of the time before infection can be expressed in terms of the solution of an integral equation, special cases of which are equivalent to the Bernoulli differential equation . Another result of the paper is that, under an appropriate scaling , the single equation of the model implies the system of three equations of the classic SIR model .
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This paper concerns a probabilistic model of
In this paper we study a discrete probabilistic SIR-type model for the
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The model is related to stochastic SIR model on graphs. We derive an integral equation for
We show that
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waiting time for an individual to get infected. In a special case the integral equation is
time before infection can be expressed in terms of the solution of an integral equation, special cases of which are
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and implies the classic SIR model
. Another result of the paper is that,
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, the single equation of the model implies the system of three equations of the classic SIR model