Behavioral response of population on transmissibility and saturation incidence of deadly pandemic through fractional order dynamical system

Abstract

The world entered in another wave of the SARS-CoV-2 due to non-compliance of standard operating procedures appropriately, initiated by respective governments. Apparently, measures like using face masks and social distancing were not observed by populace that ultimately worsens the situation. The behavioral response of the population induces a change in the dynamical outcomes of the pandemic, which is documented in this paper for all intents and purposes. The innovative perception is executed through a compartmental model with the incorporation of fractional calculus and saturation incident rate. In the first instance, the epidemiological model is designed with proportional fractional definition considering the compartmental individuals of susceptible, social distancing, exposed, quarantined, infected, isolated and recovered populations. By virtue of proportional fractional derivative, effective dynamical outcomes of equilibrium states and basic reproduction number are successfully elaborated with memory effect. The expansion of this derivative greatly simplifies the model to integer order while remaining in the fractional context. Subsequently, the memory effects on the asymptotic profiles are demonstrated through various graphical plots and tabulated values. In addition, the inclusion of saturation incident rate further explains the transmissibility of infection for different behavior of susceptible individuals. Mathematically, the results are also validated through comparative analysis of values with the solutions attained from fractional fourth order Runge-Kutta method (FRK4).

Keywords

• Quarantine
• Proportional fractional derivative
• Basic reproduction number
• fractional RK4
• Stability