Mechanistic Modeling of SARS-CoV-2 and Other Infectious Diseases and the Effects of Therapeutics

Abstract

Modern viral kinetic modeling and its application to therapeutics is a field that attracted the attention of the medical, pharmaceutical, and modeling communities during the early days of the AIDS epidemic. Its successes led to applications of modeling methods not only to HIV but a plethora of other viruses, such as hepatitis C virus (HCV), hepatitis B virus and cytomegalovirus, which along with HIV cause chronic diseases, and viruses such as influenza, respiratory syncytial virus, West Nile virus, Zika virus, and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which generally cause acute infections. Here we first review the historical development of mathematical models to understand HIV and HCV infections and the effects of treatment by fitting the models to clinical data. We then focus on recent efforts and contributions of applying these models towards understanding SARS-CoV-2 infection and highlight outstanding questions where modeling can provide crucial insights and help to optimize nonpharmaceutical and pharmaceutical interventions of the coronavirus disease 2019 (COVID-19) pandemic. The review is written from our personal perspective emphasizing the power of simple target cell limited models that provided important insights and then their evolution into more complex models that captured more of the virology and immunology. To quote Albert Einstein, "Everything should be made as simple as possible, but not simpler," and this idea underlies the modeling we describe below.

Fig. 1.. The basic model of viral infection.

Target cells, T, which are cells susceptible to infection, are infected by virus, V, with rate constant β. Target cells are assumed to be made by a source at rate s and to die at per capita rate d_T. Infected cells, I, produce virus as rate p per cell and die at rate δ per cell. Free virus particles, V, are cleared at per capita rate c.

Fig. 2.. Modeling HIV infection and treatment.

(A) The basic model can fit data (open circles) taken from individuals newly infected with HIV-1. The model solution (solid line) illustrates that virus initially grows exponentially, reaches a peak then falls and ultimately approaches a steady-state called the viral set-point. See Ref for details. (B) Biphasic decline of HIV-1 RNA after potent antiretroviral therapy is initiated. The basic model augmented with a population of long-lived infected cells (solid line) fits data taken from chronically infected HIV patients placed on combination antiretroviral therapy. The slopes of the first phase and second phase declines are mainly determined by the loss rate of short-lived and long-lived infected cells, respectively. See Ref for details.

Fig. 3.. Dynamics of HCV RNA decline after therapy initiation.

(A) Fit of Eq. (9) (solid line) to data from an HCV chronically infected patient treated with IFN given daily. After a very brief delay the viral load falls rapidly by about 1.5 log₁₀ and appears to be approaching a steady state. (B) On a longer-time scale the viral load continues to fall. The solid line shows the best-fit solution of Eqs, (1a), (1b) and (8) to the data. As discussed in Ref, the slope of the first phase decline mainly reflects the rate of viral clearance, c, whereas the slope of the second phase decline mainly reflects the rate of loss of infected cells, δ. The magnitude of the first phase decline determines the efficacy of the drug. When a more potent DAA, such as the NS5A inhibitor daclatasvir is used the first phase decline can be 3 logs, implying a drug effectiveness of 99.9%. See ref for details.

Fig. 4.. Illustration of the dynamics of SARS-CoV-2 infection in the upper respiratory tract (URT; solid red line) and the lower respiratory tract (LRT; solid blue line).

The incubation period lasts for approximately 4–6 days (5 day is shown in the figure). The virus population reaches peak viral load at or a couple of days post symptom onset. Individuals become infectious at or a few days before symptom onset. The viral load declines rapidly after peak viremia in the URT, whereas the viral load in the LRT is maintained at intermediate-to-high levels for several weeks. Dotted and dashed lines denote predicted viral load dynamics when individuals are treated with an effective antiviral (e.g. with 95% efficacy) at symptom onset (dotted lines), or 8 days post symptom onset (dashed lines). Viral load curves are drawn based on the data in Refs.^, and parameter estimates in Ref..