Infectious diseases, much like the current one of COVID-19, have had a huge economic and societal impact. The ability to model the transmission characteristics of an infection is critical to minimize its impact. In fact, predicting how fast an infection is spreading could be a major factor in deciding lockdown decisions, as well as the severity and strictness of the applied mitigation measures. Even though modeling epidemics is a well studied subject, most simple models do not include quarantine measures, such as those imposed in the recent pandemic. Our research is based on Brockmann's recent [1] paper, where a compartmental SIRX model that included two mechanisms was implemented. This model describes the delayed transmission of the infection during a pandemic. The first mechanism describes the social or individual behavioral changes during quarantine, and the second one considers that the symptomatic quarantined should be in state X - not transmitting the infection anymore.
A challenging question is whether by simulating the above model on networks we can have a result that fits well the analysis. Our process will be initially to find the parameters of the model that best fit the confirmed cases of a country, provided by Johns Hopkins University. Subsequently, the differential equations of the model will be solved applying the parameters that were computed on smaller population. This step is essential in order to compare the result to a computationally costly simulation on networks. Finally, we create the simulation and compare with the analytical results. Our results indicate that the analytical solution of the model fits to the confirmed cases during the first COVID-19 wave of all the countries we have tested. Moreover, the simulation fits adequately to the analytical solution.
References
[1] B. F. Maier, D. Brockmann, Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China, Science, (2020); https://doi.org/10.1126/science.abb4557.