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

We suggest a mathematical model for the spread of an infectious disease in human population, with particular attention to the COVID-19. Common epidemiological models, e.g., the well-known susceptible-exposed-infectious-recovered (SEIR) model, implicitly assume fast mixing of the population relative to the local infection rate, similar to the regime applicable to many chemical reactions. However, in human populations, especially under different levels of quarantine conditions, this assumption is likely to fail. We develop a continuous spatial model that includes five different populations, in which the infectious population is split into latent (or pre-symptomatic) and symptomatic. Based on nearest-neighbor infection kinetics, we arrive into a ``reaction-diffusion99 model. Our model accounts for front propagation of the infectious population domains under partial quarantine conditions, which is present on top of the common local infection process. Importantly, we also account for the variable geographic density of the population, that can strongly enhance or suppress infection spreading. Our results demonstrate how infected domains spread outward from epicenters/hotspots, leading to different regimes of sub-exponential (quasi linear or power-law) growth. Moreover, we show how weakly infected regions surrounding a densely populated area can cause rapid migration of the infection towards the center of the populated area. Predicted heat-maps show remarkable similarity to recently media released heat-maps. We further demonstrate how localized strong quarantine conditions can prevent the spreading of the disease from an epicenter/hotspot, significantly reducing the number of infected people. Application of our model in different countries, using actual demographic data and infectious disease parameters, can provide a useful predictive tool for the authorities, in particular, for planning strong lockdown measures in localized areas.