Time-dependent SI model for epidemiology and applications to Covid-19


  • Luis Arturo Urena-Lopez Departamento de Física, Universidad de Guanajuato




Epidemiological models, Bayesian statistics


A generalisation of the Susceptible-Infectious model is made to include a time-dependent transmission rate, which leads to a close analytical expression in terms of a logistic function. The solution can be applied to any continuous function chosen to describe the evolution of the transmission rate with time. Taking inspiration from real data of the Covid-19, for the case of cumulative confirmed positives and deaths, we propose an exponentially decaying transmission rate with two free parameters, one for its initial amplitude and another one for its decaying rate. The resultant time-dependent SI model, which under extra conditions recovers the standard Gompertz functional form, is then compared with data from selected countries and its parameters fit using Bayesian inference. We make predictions about the asymptotic number of confirmed positives and deaths, and discuss the possible evolution of the disease in each country in terms of our parametrisation of the transmission rate.




How to Cite

L. A. Urena-Lopez, “Time-dependent SI model for epidemiology and applications to Covid-19”, Rev. Mex. Fís., vol. 67, no. 5 Sep-Oct, pp. 050706 1–, Sep. 2021.



07 Gravitation, Mathematical Physics and Field Theory