Abstract
Fractional calculus is very convenient tool in modeling of an emergent infectious disease system comprising previous disease states, memory of disease patterns, profile of genetic variation etc. Significant complex behaviors of a disease system could be calibrated in a proficient manner through fractional order derivatives making the disease system more realistic than integer order model. In this study, a fractional order differential equation model is developed in micro level to gain perceptions regarding the effects of host immunological memory in dynamics of SARS-CoV-2 infection. Additionally, the possible optimal control of the infection with the help of an antiviral drug, viz. 2-DG, has been exemplified here. The fractional order optimal control would enable to employ the proper administration of the drug minimizing its systematic cost which will assist the health policy makers in generating better therapeutic measures against SARS-CoV-2 infection. Numerical simulations have advantages to visualize the dynamical effects of the immunological memory and optimal control inputs in the epidemic system.