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

TL;DR

This paper generalizes the SI epidemiological model to include a time-dependent transmission rate, applies it to Covid-19 data, and uses Bayesian inference to predict disease evolution and outcomes.

Contribution

It introduces a flexible, analytically solvable SI model with a decaying transmission rate tailored to Covid-19 data, enhancing predictive capabilities.

Findings

Model fits Covid-19 data from multiple countries.

Predicts asymptotic confirmed cases and deaths.

Provides insights into disease evolution based on transmission decay.

Abstract

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.