Dynamic Modeling to Identify Mitigation Strategies for Covid-19 Pandemic

Patrick Jenny; David F Jenny; Hossein Gorji; Markus Arnoldini; Wolf-Dietrich Hardt

Persons who are either infected or recovered, but were never contained, i.e., while infected, they contribute to spreading the virus. variable n s and n s,init number of susceptible and the considered population at time t = 0, respectively n i|u number of undetected infected persons n r|u number of undetected recovered persons n i|d number of detected infected persons n r|d number of detected recovered persons n k number of deceased persons n i n i|d + n i|u n r n r|d + n r|u parameter k i n s /n s,init average number of persons getting infected per day by an undetected infected person k r n i|u average number of undetected infected persons recovering per day k r n i|d average number of detected infected persons recovering per day k k n i|d average number of detected infected persons deceased per day k i n i|u average number of undetected infected persons getting detected per day T d average detection time R 0 basic reproduction number M mortality of detected population N testing interval N −1 testing frequency r fraction of susceptible persons getting tested that the virus can only be passed on by undetected infected persons. This assumption was introduced to keep the model as simple as possible without significantly changing the dynamics of the system. Moreover, latency is neglected, that is, all undetected infected persons can pass on the virus without time delay. While the model does not consider age dependency, it considers higher mortality rates due to temporary shortage of intensive care units. The graph in Fig. 1 shows the dynamic dependencies. Initially, the entire population is susceptible and can get infected. As long as Figure 1 : Graph showing the dependencies of the dynamic system describing the evolution of the numbers of undetected and detected infected persons (n i|u and n i|d , respectively), the numbers of undetected and detected recovered persons (n r|u and n r|d , respectively) and the number of fatalities (n k ). n s ≈ n s,init , the characteristic time scale (all time scales are in days) at which an infected person infects another one is 1/k i . Once n s becomes smaller, which happens quite quickly without any measures, the infection rate slows down by a factor of n s /n s,init . The rate q quantifies the number of persons being infected from outside, i.e., by travel or from the animal world. Infected persons either recover or get detected and go under quarantine, where they do not cause any further infections. It is assumed here that if someone dies, they get detected before or at time of death. In general it can be assumed that when someone falls severely ill the infected individual gets detected; an important assumption in the model is that detected persons are isolated and thus do not participate in spreading the disease. Once detected, a person recovers or deceases. All this leads to a dynamic system, which is governed by the following six ordinary differential 5 All rights reserved. No reuse allowed without permission.