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.

分数阶微积分是一种非常方便的工具，用于对包含先前疾病状态、疾病模式记忆、遗传变异概况等的突发传染病系统进行建模。疾病系统的重要复杂行为可以通过分数阶导数以熟练的方式进行校准，从而使疾病系统比整数阶模型更真实。在这项研究中，在微观层面开发了分数阶微分方程模型，以了解宿主免疫记忆对 SARS-CoV-2 感染动力学的影响。此外，在抗病毒药物的帮助下，可能对感染进行最佳控制，即。2-DG，已在此处举例说明。分数阶最优控制将使药物的适当给药最小化其系统成本，这将有助于卫生政策制定者制定更好的治疗措施来对抗 SARS-CoV-2 感染。数值模拟具有可视化流行病系统中免疫记忆和最佳控制输入的动态效应的优势。