Is the SIR model a Markov model? The article doesn't mention whether or not infection can be modeled as a Markov process, but based on the graphics it looks like it.
If I understand correctly the probabilistic infection rate is "history-less"; in other words, the probability of infecting an adjacent neighbor in the current state is not determined by the state transitions of any previous iterations.
It looks like you could model this naively with a discrete time Markov chain using a 3x3 stochastic matrix and three states: healthy, infected and deceased. I would guess you could do the same thing for the SIS model using states susceptible and infected with a 2x2 stochastic matrix instead.
In either case, modeling the epidemic as a Markov process would let you estimate the probabilities of criticality using the limit of the stochastic matrix. In fact, I think the critical threshold (probability of the epidemic going critical) will be given by left multiplying the initial probability vector by the limit of the stochastic Markov matrix.
> It looks like you could model this naively with a discrete time Markov chain using a 3x3 stochastic matrix and three states: healthy, infected and deceased.
Diffusion is a Markov process, yes. But you'd need three states per cell (not sure if that's what you meant by three states).
If I understand correctly the probabilistic infection rate is "history-less"; in other words, the probability of infecting an adjacent neighbor in the current state is not determined by the state transitions of any previous iterations.
It looks like you could model this naively with a discrete time Markov chain using a 3x3 stochastic matrix and three states: healthy, infected and deceased. I would guess you could do the same thing for the SIS model using states susceptible and infected with a 2x2 stochastic matrix instead.
In either case, modeling the epidemic as a Markov process would let you estimate the probabilities of criticality using the limit of the stochastic matrix. In fact, I think the critical threshold (probability of the epidemic going critical) will be given by left multiplying the initial probability vector by the limit of the stochastic Markov matrix.