SIR model with immigration rates
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In this simulation, we consider the stochastic evolution of a disease across anisolated system of four cities connected by roads. Note that the system repre-sents an undirected, connected graph.

Each city i will contain the disease D to a differing degree, where D is assumed to be a non-lethal disease spread by contact.

To model four unique cities with environmental variables that realistically differ such as sanitation levels and availability to medical treatment, we let the resultant infectivity a of the disease and growth rate b be unique. To introduce travel, we define travel rates to be the probability per unit time of an individual travelling from city i to j.

We examine the behaviour of the system as D evolves, whilst noting the growth of the disease in individual cities, through the use of pie charts. The fraction of susceptible, infected, and recovered citizens of each city with respect to the total population is plotted, with the corresponding proportion for the global population charted to present the state of the isolated system at any time-step.