Epidemiological model for the inhomogeneous spatial spreading of COVID-19 and other diseases

We suggest a novel mathematical framework for the inhomogeneous spatial spreading of an infectious disease in human population. SEIR-type epidemiological models assume uniform random encounters between the infectious and susceptible sub-populations, resulting in homogeneous spatial distributions. In human populations this assumption fails. Splitting the geographic region under study into areal nodes, we arrive into a continuous, ``reaction-diffusion'' model. For COVID-19, the model includes five different sub-populations. Our model accounts for the spreading evolution of infectious populations from initial epicenters, leading to different regimes of sub-exponential (e.g., power-law) growth. Importantly, we also account for the variable geographic density of the population. We show how infected ``suburban’’ areas can cause rapid migration of the infection towards a ``city’’. Predicted infection ``heat-maps" show remarkable similarity to publicly available heat-maps, e.g., from South Carolina. We further demonstrate how localized lockdown/quarantine conditions can slow down the spreading of disease from epicenters. Application of our model in different countries can provide a useful predictive tool for the authorities for planning strong lockdown measures in localized areas.