Abstract We introduce a new model for the infection of one or more subjects by a single agent and calculate the probability of infection after a fixed length of time. We model the agent and subjects as random walkers on a complete graph of N sites, jumping with equal rates from site to site. When one of the walkers is at the same site as the agent for a length of time τ, we assume that the infection probability is given by an exponential law with parameter γ, i.e. q(τ) = 1 − e^(−γτ). We introduce the boundary condition that all walkers return to their initial site (‘home’) at the end of a fixed period T. We also assume that the incubation period is longer than T so that there is no immediate propagation of the infection. In this model, we find that for short periods T, i.e. γT << 1 and T << 1, the infection probability is remarkably small and behaves like T^3. On the other hand, for large T, the probability tends to 1 (as might be expected) exponentially. However, the dominant exponential rate is given approximately by 2γ/((2+γ)N) and is therefore small for large N.

Url http://dair.dias.ie/458/

Collections Ireland -> DAIR -> Open Access DRIVERset
Ireland -> DAIR -> Type = Article
Ireland -> DAIR -> Status = Preprint