Model Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility

During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models. This document summarizes these discussions, presents difficulties, and mentions existing efforts towards future solutions that will allow future model utility and integration. We argue that without addressing these challenges, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises we face.

Initial Inoculum and the Severity of COVID-19: A Mathematical Modeling Study of the Dose-Response of SARS-CoV-2 Infections.

SARS-CoV-2 (Severe acute respiratory syndrome coronavirus 2) causes a variety of responses in those who contract the virus, ranging from asymptomatic infections to acute respiratory failure and death. While there are likely multiple mechanisms triggering severe disease, one potential cause of severe disease is the size of the initial inoculum. For other respiratory diseases, larger initial doses lead to more severe outcomes. We investigate whether there is a similar link for SARS-CoV-2 infections using the combination of an agent-based model (ABM) and a partial differential equation model (PDM). We use the model to examine the viral time course for different sizes of initial inocula, generating dose-response curves for peak viral load, time of viral peak, viral growth rate, infection duration, and area under the viral titer curve. We find that large initial inocula lead to short infections, but with higher viral titer peaks; and that smaller initial inocula lower the viral titer peak, but make the infection last longer.

Estimation of virus-mediated cell fusion rate of SARS-CoV-2.

Several viruses have the ability to form large multinucleated cells known as syncytia. Many properties of syncytia and the role they play in the evolution of a viral infection are not well understood. One basic question that has not yet been answered is how quickly syncytia form. We use a novel mathematical model of cell-cell fusion assays and apply it to experimental data from SARS-CoV-2 fusion assays to provide the first estimates of virus-mediated cell fusion rate. We find that for SARS-CoV2, the fusion rate is in the range of 6 × 10-4-12×10-4/h. We also use our model to compare fusion rates when the protease TMPRSS2 is overexpressed (2-4 times larger fusion rate), when the protease furin is removed (one third the original fusion rate), and when the spike protein is altered (1/10th the original fusion rate). The use of mathematical models allows us to provide additional quantitative information about syncytia formation.

Epidemiological Consequences of Viral Interference: A Mathematical Modeling Study of Two Interacting Viruses.

Some viruses have the ability to block or suppress growth of other viruses when simultaneously present in the same host. This type of viral interference or viral block has been suggested as a potential interaction between some respiratory viruses including SARS-CoV-2 and other co-circulating respiratory viruses. We explore how one virus' ability to block infection with another within a single host affects spread of the viruses within a susceptible population using a compartmental epidemiological model. We find that population-level effect of viral block is a decrease in the number of people infected with the suppressed virus. This effect is most pronounced when the viruses have similar epidemiological parameters. We use the model to simulate co-circulating epidemics of SARS-CoV-2 and influenza, respiratory syncytial virus (RSV), and rhinovirus, finding that co-circulation of SARS-CoV-2 and RSV causes the most suppression of SARS-CoV-2. Paradoxically, co-circulation of SARS-CoV-2 and influenza or rhinovirus results in almost no change in the SARS-CoV-2 epidemic, but causes a shift in the timing of the influenza and rhinovirus epidemics.

Treatment of Respiratory Viral Coinfections.

With the advent of rapid multiplex PCR, physicians have been able to test for multiple viral pathogens when a patient presents with influenza-like illness. This has led to the discovery that many respiratory infections are caused by more than one virus. Antiviral treatment of viral coinfections can be complex because treatment of one virus will affect the time course of the other virus. Since effective antivirals are only available for some respiratory viruses, careful consideration needs to be given on the effect treating one virus will have on the dynamics of the other virus, which might not have available antiviral treatment. In this study, we use mathematical models of viral coinfections to assess the effect of antiviral treatment on coinfections. We examine the effect of the mechanism of action, relative growth rates of the viruses, and the assumptions underlying the interaction of the viruses. We find that high antiviral efficacy is needed to suppress both infections. If high doses of both antivirals are not achieved, then we run the risk of lengthening the duration of coinfection or even of allowing a suppressed virus to replicate to higher viral titers.

Estimation of viral kinetics model parameters in young and aged SARS-CoV-2 infected macaques.

The SARS-CoV-2 virus disproportionately causes serious illness and death in older individuals. In order to have the greatest impact in decreasing the human toll caused by the virus, antiviral treatment should be targeted to older patients. For this, we need a better understanding of the differences in viral dynamics between SARS-CoV-2 infection in younger and older adults. In this study, we use previously published averaged viral titre measurements from the nose and throat of SARS-CoV-2 infection in young and aged cynomolgus macaques to parametrize a viral kinetics model. We find that all viral kinetics parameters differ between young and aged macaques in the nasal passages, but that there are fewer differences in parameter estimates from the throat. We further use our parametrized model to study the antiviral treatment of young and aged animals, finding that early antiviral treatment is more likely to lead to a lengthening of the infection in aged animals, but not in young animals.

Quantifying the effect of trypsin and elastase on in vitro SARS-CoV infections.

The SARS coronavirus (SARS-CoV) has the potential to cause serious disease that can spread rapidly around the world. Much of our understanding of SARS-CoV pathogenesis comes from in vitro experiments. Unfortunately, in vitro experiments cannot replicate all the complexity of the in vivo infection. For example, proteases in the respiratory tract cleave the SARS-CoV surface protein to facilitate viral entry, but these proteases are not present in vitro. Unfortunately, proteases might also have an effect on other parts of the replication cycle. Here, we use mathematical modeling to estimate parameters characterizing viral replication for SARS-CoV in the presence of trypsin or elastase, and in the absence of either. In addition to increasing the infection rate, the addition of trypsin and elastase causes lengthening of the eclipse phase duration and the infectious cell lifespan.

SARS-CoV-2 coinfections: Could influenza and the common cold be beneficial?

The novel coronavirus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has rapidly spread around the world, causing serious illness and death and creating a heavy burden on the healthcare systems of many countries. Since the virus first emerged in late November 2019, its spread has coincided with peak circulation of several seasonal respiratory viruses, yet some studies have noted limited coinfections between SARS-CoV-2 and other viruses. We use a mathematical model of viral coinfection to study SARS-CoV-2 coinfections, finding that SARS-CoV-2 replication is easily suppressed by many common respiratory viruses. According to our model, this suppression is because SARS-CoV-2 has a lower growth rate (1.8/d) than the other viruses examined in this study. The suppression of SARS-CoV-2 by other pathogens could have implications for the timing and severity of a second wave.

Quantifying the effect of remdesivir in rhesus macaques infected with SARS-CoV-2.

The world is in the midst of a pandemic caused by a novel coronavirus and is desperately searching for possible treatments. The antiviral remdesivir has shown some effectiveness against SARS-CoV-2 in vitro and in a recent animal study. We use data from a study of remdesivir in rhesus macaques to fit a viral kinetics model in an effort to determine the most appropriate mathematical descripton of the effect of remdesivir. We find statistically significant differences in the viral decay rate and use this to inform a possible mathematical formulation of the effect of remdesivir. Unfortunately, this model formulation suggests that the application of remdesivir will lengthen SARS-CoV-2 infections, putting into question its potential clinical benefit.

Modeling the role of asymptomatics in infection spread with application to SARS-CoV-2.

SARS-CoV-2 started causing infections in humans in late 2019 and has spread rapidly around the world. While the number of symptomatically infected and severely ill people is high and has overwhelmed the medical systems of many countries, there is mounting evidence that some of the rapid spread of this virus has been driven by asymptomatic infections. In this study, we use a compartmental mathematical model of a viral epidemic that includes asymptomatic infection to examine the role of asymptomatic individuals in the spread of the infection. We apply the model to epidemics in California, Florida, New York, and Texas, finding that asymptomatic infections far outnumber reported symptomatic infections at the peak of the epidemic in all four states. The model suggests that relaxing of social distancing measures too quickly could lead to a rapid rise in the number of cases, driven in part by asymptomatic infections.