Inhomogeneous Transmission and Asynchronic Mixing in the Spread of COVID-19 Epidemics

The ongoing epidemic of COVID-19 first found in China has reinforced the need to develop epidemiological models capable of describing the progression of the disease to be of use in the formulation of mitigation policies. Here, this problem is addressed using a metapopulation approach to consider the inhomogeneous transmission of the spread arising from a variety of reasons, like the distribution of local epidemic onset times or of the transmission rates. We show that these contributions can be incorporated into a susceptible-infected-recovered framework through a time-dependent transmission rate. Thus, the reproduction number decreases with time despite the population dynamics remaining uniform and the depletion of susceptible individuals is small. The obtained results are consistent with the early subexponential growth observed in the cumulated number of confirmed cases even in the absence of containment measures. We validate our model by describing the evolution of COVID-19 using real data from different countries, with an emphasis in the case of Mexico, and show that it also correctly describes the longtime dynamics of the spread. The proposed model yet simple is successful at describing the onset and progression of the outbreak, and considerably improves the accuracy of predictions over traditional compartmental models. The insights given here may prove to be useful to forecast the extent of the public health risks of the epidemics, thus improving public policy-making aimed at reducing such risks.