Mathematical simulation of the evolution of the Covid-19 epidemic in the Metrropolitan Zone of Lima-Callao

Abstract

This paper presents a mathematical model that simulates the evolution of health cases as a consequence of an infection with the coronavirus taking as reference the daily reports issued by the Ministry of Health for the whole Peruvian territory. In this work we put emphasis on the Metropolitan Area of Lima-Callao. For this purpose four probabilistic parameters are used, whose values are chosen in such a way that the model reproduces the reported number of cases. One of them quantifies the probability that a person can be infected per passing day, the second parameter the probability of recovering per passing day since the date the infection took place. The other two parameters are related to the probability of recovering or dying per each passing day. In this modeling two intervals of time are considered: an initial interval of 75 days during which the rate of infections is accelerated followed by an interval in which the rate of infections coincides with the final value of the first interval. The fitting of these parameters to the reported values give as result that the average numbers of days required for recovery is 27 days since the date of infection. Another result is that the maximum number of recovering patients will be about 115 thousand within six months, a fraction of which will require hospital care. The death rate used is 8%.