A Continuous Commuter Model for the Spread of Infectious Disease

Once an infectious disease has entered a population, the dynamics are dominated by local interactions among citizens. Infection spread is often modeled by adding diffusion terms to a compartmental model, suggesting that individuals diffuse in their environment, but these models do not conserve local population. Our proposed model gives individuals a well-defined home but allows them to make contact with others and spread disease at destinations not too far from home according to a commuting probability function. The localized nature of daily commutes allows us to derive a continuous, spatially resolved SIR model with diffusion that is independent of the exact form of the commuting probabilities. The infected diffusion coefficient is positive and proportional to the characteristic commuting length while the susceptible diffusion coefficient is negative, emphasizing the fact that the disease diffuses rather than the individuals. Fisher waves are observed, but unlike in the simplest reaction-diffusion epidemic models, there is an additional drift term that increases the rate at which disease spreads from populated cities. Our commuter model can provide intuition about expected patterns of disease transmission in more complicated and noisy real-world epidemics.