Periodic dynamics of rubella epidemic under standard and fractional Caputo operator with real data from Pakistan

Memory effects of epidemics play a vital role in mathematical models of infectious diseases. In this research study, an epidemiological SEIR (Susceptible, Exposed, Infectious, Removed) type model for the rubella epidemic has been proposed via classical and fractional order Caputo differential operators while assuming the periodic transmission rate beta(t). The Caputo model has been investigated for the existence and uniqueness of its solutions via fixed point theory while the unique non-negative solution remains bounded within the biologically feasible region. Later, the non-fixed biological parameters of the classical and the Caputo model are obtained via nonlinear least squares fitting technique taking the real monthly cases for the rubella epidemic in Pakistan for the period 2010-2012. The performance rate of the Caputo model is 35% higher than that of the model with integer order derivative. The numerical simulations are obtained under different cases and it is highly suggested that the infectious rate sigma must be controlled as much as possible to eradicate the rubella epidemic. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.