The unprecedented Covid-19 pandemic has resulted in more than 14.75 million infections and 6, 10, 839 deaths in 212 countries. Appropriate interventions can decrease the rate of Covid-19 related mortality. Fast track clinical trials around the world are addressing the efficacy of individual pharmaceutical agent acting at various stages of pathogenesis. However, lessons learnt while dealing with past viral epidemics mandates, simultaneous use of such drugs in combination amongst different populations. Mathematical modelling studies can be extremely helpful in understanding the efficacy of drugs both individually and in combination. The current within-host mathematical model studies the natural history of Covid-19 in terms of complex interplay of virus replication and behaviour of host immune response. Additionally it studies the role of various drugs at various stages of pathogenesis. The model was validated by generating two-parameter heat plots, representing the characteristics of Covid-19, the sensitivity analysis identified the crucial parameters. The efficacy of interventions was assessed by optimal control problem. The model dynamics exhibited disease-free equilibrium and the infected equilibrium with their stability, based on the reproduction number $R_0$, the transcritical bifurcation observed at $R_0=1$. The burst rate and the natural death rate of the virus were observed as most significant parameters in the life-threatening Covid-19 pneumonia. The antiviral drugs affecting viral replication and those modulating the immune response, reduce the infected cells and viral load significantly. However, the yield was optimal and most effective when the combination therapy involving one or more antiviral and one or more immunomodulating drugs were administered together. These findings may help physicians with early decision making in treatment of life-threatening Covid-19 infection.

前所未有的Covid-19大流行在212个国家/地区造成超过1475万例感染，并导致6、10、839人死亡。适当的干预措施可以降低Covid-19相关死亡率。世界各地的快速临床试验都致力于解决单个药物在发病机理各个阶段的作用。但是，在应对过去的病毒流行规定时吸取的教训是，在不同人群中同时使用此类药物。数学模型研究对于单独或组合使用药物的功效非常有用。当前的宿主内数学模型根据病毒复制的复杂相互作用和宿主免疫反应的行为研究Covid-19的自然历史。此外，它研究了各种药物在发病机理各个阶段的作用。该模型通过生成代表Covid-19特征的两参数热图进行了验证，灵敏度分析确定了关键参数。通过最佳控制问题评估干预措施的有效性。基于繁殖数，模型动力学表现出无病平衡和感染平衡及其稳定性${\mathrm{[R}}_0$，在 ${\mathrm{[R}}_0=\mathrm{1个}$。在威胁生命的Covid-19肺炎中，病毒的爆发率和自然死亡率是最重要的参数。影响病毒复制的抗病毒药物和调节免疫反应的抗病毒药物可显着减少感染的细胞和病毒载量。但是，当同时使用一种或多种抗病毒药物和一种或多种免疫调节药物的联合治疗时，收率是最佳且最有效的。这些发现可能有助于医生及早作出决定，以治疗威胁生命的Covid-19感染。