Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

Abstract The earlier analytical analysis (part A) of the susceptible–infectious–recovered (SIR) epidemics model for a constant ratio k infection to recovery rates is extended here semi-time case which particularly appropriate modeling temporal evolution later (than first) pandemic waves when greater population fraction from first wave has been infected. In SIR does not describe quantities in past; instead they only hold times than initial time t = 0 newly occurring wave. Simple exact and approximative expressions are derived final maximum values infected, susceptible recovered/removed fractions as well daily rate cumulative number new infections. It demonstrated that two types infections j ( τ ) occur depending on value infected I (0) η : decay ⩾ 1 − 2 monotonically decreases at all positive its (1 ). Alternatively, peak < attains finite time. By comparing approximated solutions J with ones obtained by numerical integration, it shown approximations accurate within most 2.5 percent. found persons sensitively influences late dependence epidemics, Such dependencies do exist investigated all-time case.