A mathematical model for the study and analysis of the dynamics of COVID-19 in Colombia

Abstract

A mathematical model is presented to analyze the dynamics of COVID-19, which is based on the SEIR model and includes the subpopulations of asymptomatic (A), hospitalized (H) and deceased (D), for which it is called SEAIHRD. The proposed model has been validated with data reported in Colombia during the period of time of the epidemic prior to the end of mandatory preventive isolation, as well as for the definition of parameters that also include performed estimations in previous works associated to the dynamics of transmission of the virus. The mathematical model was implemented
in Python for the solution of the system of ordinary differential equations in three different scenarios of the dynamics of the disease for the computational simulation: 1) without restriction measures (do nothing), 2) with moderate measures, and 3) with strong measures. The qualitative results suggest a behavior similar to that reported by data from the National Institute of Health of Colombia and show the consequences of extreme scenarios, that is, of not having done anything or if very strong restrictive Susmeasures had been implemented. The population dynamics of the model is close to the real one, allowing the estimation of spikes of contagion and infected cases, as well as the potential population that will require hospitalization or end up dead. Finally, the proposed mathematical model makes a compromise between simplicity and affinity to the behavior of the disease dynamics for its potential adaptation in other subpopulations or regions of the country.