Abstract— SARS-CoV-2 has emerged to cause the outbreak of COVID-19, which has expanded into a worldwide human pandemic. Although detailed experimental data on animal experiments would provide insight into drug efficacy, the scientists involved in these experiments would be exposed to severe risks. In this context, we propose a computational framework for studying infection dynamics that can be used to capture the growth rate of viral replication and lung epithelial cell in presence of SARS-CoV-2. Specifically, we formulate the model consisting of a system of non-linear ODEs that can be used for visualizing the infection dynamics in a cell population considering the role of T cells and Macrophages. The major contribution of the proposed simulation method is to utilize the infection progression model in testing the efficacy of the drugs having various mechanisms and analyzing the effect of time of drug administration on virus clearance. Clinical Relevance—The proposed computational framework incorporates viral infection dynamics and role of immune response in Covid-19 that can be used to test the impact of drug efficacy and time of drug administration on infection mitigation. I. INTRODUCTION In December 2019, a serious outbreak occurred in China due to coronavirus, which is named as the novel COVID-19. The novel COVID-19, which caused this infection belongs to the family of SARS, a Severe Acute Respiratory Syndrome (SARS-CoV) [1]. The SARS-CoV-2 exponentially expanded across the globe into a human pandemic. Patients with severe infection suffer from acute respiratory distress, resulting in multiple organ failures and fatality. Coronaviruses are enveloped positive-stranded RNA viruses, and generally infect the epithelial cells in the respiratory and gastrointestinal tract. COVID-19 is a highly contagious disease indicating the need for widespread vaccination. In the absence of any effective drug with an unknown epidemiological life cycle, mathematical models are crucial for studying various pathophysiological processes and immunological responses of real-world problems. By using mathematical models for these processes, information on drug efficacy can be obtained [2], [3]. In this context, we plan to build a computational framework for visualizing SARS-CoV-2 infection dynamics in presence of immune response and analyzing the effect of drug efficacy on virus clearance (Figure 1). To achieve this, an ODE model *Research supported by Indian Institute of Technology Hyderabad, Telangana, India Surbhi Sharma is with the Department of Chemical Engineering, IIT Hyderabad, Sangareddy, India (e-mail: ch17resch11001@iith.ac.in) Abha Saxena is with the Department of Chemical Engineering, IIT Hyderabad, Sangareddy, India (e-mail: ch15resch11001@iith.ac.in) system was developed which was validated from the experimental data collected on growth of SARS-CoV-2 from throat swab samples [4]. Additionally, the model includes the response of adaptive and innate immune system, which was validated using bronchoalveolar lavage fluid (BALF) sample obtained from patients with moderate and severe COVID-19 infections [5]. The existing mathematical models for viral infection are mostly target-cell limited models that have been developed to understand the mechanism of viral infection inside the host cells [2], [3], [6]. These model variables generally include: uninfected target cells, which in the case of SARS-CoV-2 infection is the lung epithelial cells, infected target cells, which are capable of producing virus particles and the virus particle itself. None of the previous models incorporate the dynamics of T cells and macrophages in regulation of the infection progression. In order to identify the contribution of T cells and Macrophages, firstly, we formulate and compare two models where model 1 (EIVT mode) considers E, representing uninfected epithelial cells, I representing infected epithelial cells, V representing virus and T representing T cells. Whereas model 2 (EIVTM model) consists of a fifth entitiy M, representing the macrophages along with the variables considered in EIVT model. Secondly, parameter estimation was performed using sequential quadratic programming Soumita Chel, is with the Department of Chemical Engineering, IIT Hyderabad, Sangareddy, India (e-mail: csesoumita@gmail.com) Kishalay Mitra, is with the Department of Chemical Engineering, IIT Hyderabad, Sangareddy, India (e-mail: kishalay@iith.ac.in) Lopamudra Giri is with the Department of Chemical Engineering, IIT Hyderabad, Sangareddy, India (Corresponding author, phone number: +91- 40-2301-7024, e-mail: giril@iith.ac.in) Surbhi Sharma, Abha Saxena, Soumita Chel, Kishalay Mitra, Lopamudra Giri Mathematical modeling of viral infection dynamics and immune response in SARS-CoV-2: A computational framework for testing drug efficacy Figure 1. Graphical abstract of the workflow. The interaction between different model variables and the description of the data used for the model is shown. 2021 43rd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC) Oct 31 - Nov 4, 2021. Virtual Conference 978-1-7281-1178-0/21/$31.00 ©2021 IEEE 4370