Kröger, M.; Schlickeiser, R. SIR-Solution for Slowly Time-Dependent Ratio between Recovery and Infection Rates. Physics 2022, 4, 504–524, doi:10.3390/physics4020034.
Kröger, M.; Schlickeiser, R. SIR-Solution for Slowly Time-Dependent Ratio between Recovery and Infection Rates. Physics 2022, 4, 504–524, doi:10.3390/physics4020034.
Kröger, M.; Schlickeiser, R. SIR-Solution for Slowly Time-Dependent Ratio between Recovery and Infection Rates. Physics 2022, 4, 504–524, doi:10.3390/physics4020034.
Kröger, M.; Schlickeiser, R. SIR-Solution for Slowly Time-Dependent Ratio between Recovery and Infection Rates. Physics 2022, 4, 504–524, doi:10.3390/physics4020034.
Abstract
The temporal evolution of pandemics described by the susceptible-infectious-recovered (SIR)-compartment model is sensitively determined by the time dependence of the infection (a(t)) and recovery (u(t)) rates regulating the transitions from the susceptible to the infected and from the infected to the recovered compartment, respectively. Here approximated SIR-solutions for different time dependencies of the infection and recovery rates are derived which are based on the adiabatic approximation assuming time-dependent ratios k(t)=u(t)/a(t) varying slowly in comparison to the typical time characteristics of the pandemic wave. For such slow variations the available analytical approximations from the KSSIR-model, valid for a stationary value of the ratio k, are used to insert a-posteriori the adopted time-dependent ratio of the two rates. Instead of investigating endless different combinations of the time dependencies of the two rates a(t) and u(t) a suitably parameterized reduced time dependence of the ratio k(tau) is adopted. Together with the definition of the reduced time this parameterized ratio k(tau) allows us to cover a great variety of different time dependencies of the infection and recovery rates. The agreement between the solutions from the adiabatic approximation in its four different studied variants and the exact numerical solutions of the SIR-equations is remarkably good providing strong confidence in the accuracy of the proposed adiabatic approximation.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
