Discontinuity of the deadly infection rate for the COVID-19 pandemia due to lockdown measures

Sabio Vera, A.

An asymmetric version of the classical Kermack-McKendrick description of an epidemic evolution is presented in terms of four independent parameters. This is enough to obtain an accurate description of the different stages of the COVID-19 pandemia in any country for the reported daily and total number of casualties due to the infection. The asymmetry accounts for lockdown effects introduced to reduce the impact of the epidemic outburst. A set of new variables allows for an analytic study of the evolution of the system before and after the lockdown measures are put in place. A continuous matching is possible for all variables in the system apart from the time dependence of the infection rate. An analytic expression is obtained for this discontinuity which is proposed as a good quantity to gauge the efficiency of the lockdown measures. A study of this variable for different countries is performed.