key: cord-0743578-5cd211nx authors: Desikan, Rajat; Padmanabhan, Pranesh; Kierzek, Andrzej M.; van der Graaf, Piet H. title: Mechanistic Models of COVID-19: Insights into Disease Progression, Vaccines, and Therapeutics date: 2022-05-16 journal: Int J Antimicrob Agents DOI: 10.1016/j.ijantimicag.2022.106606 sha: 48e5ab7775efc7702931cd21e56fb292ef4212f9 doc_id: 743578 cord_uid: 5cd211nx The COVID-19 pandemic has severely impacted health systems and economies worldwide. Significant global efforts are therefore ongoing to improve vaccine efficacies, optimize vaccine deployment, and develop new antiviral therapies to combat the pandemic. Mechanistic viral dynamics and quantitative systems pharmacology models of SARS-CoV-2 infection, vaccines, immunomodulatory agents, and antiviral therapeutics have played a key role in advancing our understanding of SARS-CoV-2 pathogenesis and transmission, the interplay between innate and adaptive immunity to influence the outcomes of infection, effectiveness of treatments, mechanisms and performance of COVID-19 vaccines, and the impact of emerging SARS-CoV-2 variants. Here, we review some of the critical insights provided by these models and discuss the challenges ahead. COVID-19, caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus, has infected more than half a billion individuals worldwide, resulting in the death of over 6.2 million people as of 26 th April 2022. SARS-CoV-2 is a small, single-stranded RNA virus that primarily infects the respiratory system. The clinical outcome of infection is heterogeneous, ranging from cure without symptoms to severe disease culminating in death [1] . Nearly two dozen COVID-19 vaccines have been approved for clinical use, with several hundreds of candidates in clinical and preclinical development [2] . The approved vaccines are powerful in conferring protection, particularly against severe disease [3] . Simultaneously, new antivirals such as paxlovid and Nirmatrelvir have been shown to significantly reduce COVID-19 deaths in clinical trials [4, 5] . As SARS-CoV-2 continues to evolve, enormous efforts are therefore underway to understand how SARS-CoV-2 variants may impact vaccine and antiviral treatment effectiveness [6, 7] . Over the past two years, SARS-CoV-2 viral dynamic models that quantitatively analyze viral load evolution in patients (Figure 1 ), and quantitative systems pharmacology (QSP) models that integrate systems biology and human physiology with clinical pharmacology (Figure 2a, b) and can thus predict the system's response to therapeutics, have been developed. These models are playing a key role in understanding SARS-CoV-2 infection as well as identifying optimal vaccine dosing regimen and antiviral treatment strategies. In this review, we first discuss insights gained into COVID-19 disease progression and the influence of host immune responses on suppressing infection. Next, we focus on modelling COVID-19 therapeutics, followed by descriptions of vaccine QSP frameworks for dose optimization and predicting efficacy. Finally, we conclude by outlining modelling efforts needed to combat the current and future pandemics. Like many acute viral infections, multiple clinical [8] [9] [10] [11] [12] and non-clinical studies [13] (some with very high temporal resolution) have shown that COVID-19 is mainly characterized by two phases (Figure 1a ): a proliferation phase, where viral loads at sites of infection increase exponentially due to abundant target cells until it attains a peak, and a clearance phase, where a lack of target cells and/or mounted antiviral host immune responses lower and clear the virus from the system [9] . The relative timescales of the two phases, and (Figure 1a Therefore, mathematical modelling of longitudinal virus load data has been employed to not only quantitatively determine in vivo disease dynamics at the individual and population levels, but also the interplay between virus-host immune responses and the resulting pathology. Statistical models are a class of models employed for quantifying SARS-CoV-2 virus dynamics, where virus load time series measured using RT-qPCR are fit to piecewise linear regression or other models to estimate individual and population virus trajectories (Figure 1a ) [9] . While such phenomenological models were useful for deployment in the initial stages of the pandemic with limited available data, a glaring limitation is a lack of mechanistic insight into disease progression, co-evolving immune dynamics, heterogeneity of responses, and estimates of efficacies of various therapeutics and vaccines. More mechanistic virus dynamics models [8, 14] (Figure 1b) largely address the above limitations and have provided valuable insights into the progression of many acute and chronic infections caused by HIV [8, 15] , hepatitis C virus (HCV) [16] , influenza [17, 18] , and Zika virus [19] among others. Example model fits to SARS-CoV-2 virus trajectories from two patients are shown in Figure 1c . For instance, in hamster models challenged with SARS-CoV-2, early prophylactic interferon treatment conferred protection whereas later treatment did not [29] . Future modelling efforts, especially larger QSP models [30] [31] [32] incorporating viral dynamics and associated innate and adaptive immune responses at various anatomical sites while accounting for host factors such as comorbidities and age, may accurately predict how different arms of the immune system would interact to determine diverse infection outcomes and guide rational optimization of treatments with immune modulators. An obstacle with developing larger disease models incorporating the immune response is that, often, detailed kinetics are only available for viral load measurements while immune cell count spatio-temporal dynamics, which are mechanistically intertwined with pathogen and disease dynamics, are harder or near impossible to obtain, especially from deeper tissues. Therefore, this is a common issue with many disease models and perhaps a grand challenge [15] ). Lastly, experiments with animal models may yield immune response dynamics even in solid tissues, but this must be carefully interpreted given that such models typically do not capture all aspects of human infection. Mathematical models combining virus dynamics with pharmacokinetic/pharmacodynamic (PK/PD) models of therapeutics have been extensively used to estimate the efficacy and identify the mechanism(s) of action of therapeutics ( Figure 1b ). Models achieve this by introducing an efficacy factor varying between 0 and 1 that lowers viral production or de novo infection rate constants depending on the mode of drug action [14] . For instance, Pfizer's paxlovid and nirmatrelvir, which work by inhibiting the activity of SARS-CoV-2 protease [4, 5] , would lower the viral production rates in the model (Figure 1b) . Similarly, Merck's molnupiravir, which may inhibit viral replication by increasing viral mutation rates [4] , would render a fraction of progeny virions non-infectious [8, 36] . Anti-SARS-CoV-2 neutralizing monoclonal antibody drugs such as REGEN-COV (casirivimab and imdevimab), sotrovimab, bamlanivimab, and etesevimab, block infection of target cells and simultaneously induce phagocytosis and clearance of virus. We expect that analyzing viral kinetics in patients treated with these antivirals in the future will: (i) quantify the treatment efficacies, (ii) clarify the in vivo dominant mechanism(s) of action of these antivirals, (iii) optimize dosage, as shown recently for the combination of bamlanivimab and etesevimab using population PK/PD and viral dynamics modeling [37, 38] , and, (iv) predict optimal antiviral combinations with high genetic barriers [8] that may lower the probability of emerging drug-resistant variants, akin to HIV and HCV combination therapies. Several models have predicted the need for early administration before the viral peak of therapeutics that blocked new infections or lowered viral production, as most cells are likely to be infected by the time viral load peaks, and late administration is likely to inhibit only a small proportion of cellular infection [20, 21, 32, 39] . The current estimates of the critical therapeutic efficacy, which is the minimum drug efficacy above which infection cannot be established, is ~80-95%. Until effective SARS-CoV-2 therapeutics are developed, one strategy would be to repurpose available drugs for treatment. However, analysis of SARS-CoV-2 dynamics in patients treated with different repurposed drugs revealed the efficacies were far below the critical efficacy [21] . Therefore, combination treatments that display synergistic effects are desirable [40] . We recently developed a model of SARS-CoV-2 entry into target cells and predicted that targeting two host proteases, which mediated SARS-CoV-2 entry into target cells via independent pathways, could be synergistic [41] . Such frameworks can be advantageously combined with mathematical models of drug resistance to elucidate optimal combination therapies that would simultaneously maximize synergy and minimize the probability of escape variants. With a raging pandemic, no definitive sterilizing cure (yet), and substantial vulnerable populations worldwide, regulatory-approved COVID-19 vaccines are critical for safely suppressing infections and mortality. In the current scenario with many variables such as limited vaccine supplies, availability of multiple vaccine types with varying levels of protection proprietary, vaccine QSP model [43] (Figure 2b) , which was extensively calibrated with preclinical and clinical mRNA vaccine data, to predict that a longer 7-8-week prime-boost interval would elicit maximal antibody titers, and reassuringly, a 12-week interval would still yield higher titers than a 3-or 4-week interval (Figure 2c) . Strikingly, ~6 months after this prediction, the PITCH study [48] performed by employing an extended dosing interval of 6-14 weeks with the Pfizer/BioNTech vaccine quantitatively confirmed this prediction [49] , highlighting the power of QSP frameworks to robustly forecast what-if scenarios in the face of uncertainty. The neutralization potential of the elicited antibodies may also be improved with delayed boost dosing (and/or lowered prime dose) due to altered B cell selection stringency in germinal centers [45] . Next, we discuss other important questions about which QSP predictions can help ameliorate uncertainty and thus significantly contribute to decision-making. Do the elderly mount less effective immune responses upon vaccination? Extensive simulations with QSP models calibrated on age-stratified clinical trial data suggested reduced antibody titers in the elderly (65-85 years) [43] . The reduction was exacerbated at lower vaccine doses, and with time due to waning immune responses [43] . Thus, multiple boosters with current vaccine doses may be necessary for the elderly, especially with the rise of variants. On the other hand, increasing prime and boost antigen dose amounts in the elderly may elicit comparable antibody titers to that within younger individuals, suggesting that age-stratified What is the relationship between immune responses evoked by vaccination and protection against infection? To answer this, immune correlates of protection must be identified [51] . While cellular responses such as primed T cells undoubtedly confer some protection, neutralizing antibody (NAb) titers, usually the first line of defense against SARS-CoV-2 viruses and infection in vaccinated individuals, appears to be a robust immune correlate of vaccine efficacy from statistical analyses of clinical and epidemiological data [51] [52] [53] . Higher the NAb titers elicited by a vaccine, higher the protection accorded to the population immunized by that vaccine [52] . A mechanistic link between NAb titers and protection, which would unravel the mechanistic underpinnings of COVID-19 vaccine efficacies and enable robust efficacy predictions, was recently proposed by us [12, 54] . First, we hypothesized that inter-individual variability in NAb responses upon vaccination can be described by assuming that the elicited We anticipate that the optimal development and deployment of therapeutics and vaccines, especially in times of urgent need such as global pandemics, would be greatly accelerated by integrated, semi-mechanistic/statistical, population-based models. 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We thank Prof. Narendra M. Dixit for discussions and critically evaluating our manuscript. All authors were involved in conceptualizing the study, analysis, interpretation of data, and revisions. Writing of the first draft: R.D. and P.P. All authors have given final approval of the manuscript. Equal contributions: R.D. and P.P.