Heterogeneous SARS-CoV-2 kinetics due to variable timing and intensity of immune responses.

The viral kinetics of documented SARS-CoV-2 infections exhibit a high degree of inter-individual variability. We identified six distinct viral shedding patterns, which differed according to peak viral load, duration, expansion rate and clearance rate, by clustering data from 768 infections in the National Basketball Association cohort. Omicron variant infections in previously vaccinated individuals generally led to lower cumulative shedding levels of SARS-CoV-2 than other scenarios. We then developed a mechanistic mathematical model that recapitulated 1510 observed viral trajectories, including viral rebound and cases of reinfection. Lower peak viral loads were explained by a more rapid and sustained transition of susceptible cells to a refractory state during infection, as well as an earlier and more potent late, cytolytic immune response. Our results suggest that viral elimination occurs more rapidly during omicron infection, following vaccination, and following re-infection due to enhanced innate and acquired immune responses. Because viral load has been linked with COVID-19 severity and transmission risk, our model provides a framework for understanding the wide range of observed SARS-CoV-2 infection outcomes.

Two-way pharmacodynamic modeling of drug combinations and its application to pairs of repurposed Ebola and SARS-CoV-2 agents.

Existing pharmacodynamic (PD) mathematical models for drug combinations discriminate antagonistic, additive, multiplicative, and synergistic effects, but fail to consider how concentration-dependent drug interaction effects may vary across an entire dose-response matrix. We developed a two-way pharmacodynamic (TWPD) model to capture the PD of two-drug combinations. TWPD captures interactions between upstream and downstream drugs that act on different stages of viral replication, by quantifying upstream drug efficacy and concentration-dependent effects on downstream drug pharmacodynamic parameters. We applied TWPD to previously published in vitro drug matrixes for repurposed potential anti-Ebola and anti-SARS-CoV-2 drug pairs. Depending on the drug pairing, the model recapitulated combined efficacies as or more accurately than existing models and can be used to infer efficacy at untested drug concentrations. TWPD fits the data slightly better in one direction for all drug pairs, meaning that we can tentatively infer the upstream drug. Based on its high accuracy, TWPD could be used in concert with PK models to estimate the therapeutic effects of drug pairs in vivo.

A unifying model to explain high nirmatrelvir therapeutic efficacy against SARS-CoV-2, despite low post-exposure prophylaxis efficacy and frequent viral rebound.

In a pivotal trial (EPIC-HR), a 5-day course of oral ritonavir-boosted nirmatrelvir, given early during symptomatic SARS-CoV-2 infection (within three days of symptoms onset), decreased hospitalization and death by 89.1% and nasal viral load by 0.87 log relative to placebo in high-risk individuals. Yet, nirmatrelvir/ritonavir failed as post-exposure prophylaxis in a trial, and frequent viral rebound has been observed in subsequent cohorts. We developed a mathematical model capturing viral-immune dynamics and nirmatrelvir pharmacokinetics that recapitulated viral loads from this and another clinical trial (PLATCOV). Our results suggest that nirmatrelvir's in vivo potency is significantly lower than in vitro assays predict. According to our model, a maximally potent agent would reduce the viral load by approximately 3.5 logs relative to placebo at 5 days. The model identifies that earlier initiation and shorter treatment duration are key predictors of post-treatment rebound. Extension of treatment to 10 days for Omicron variant infection in vaccinated individuals, rather than increasing dose or dosing frequency, is predicted to lower the incidence of viral rebound significantly.

Modeling and prediction of phase shifts in noisy two-cycle oscillations.

Understanding and predicting ecological dynamics in the presence of noise remains a substantial and important challenge. This is particularly true in light of the poor quality of much ecological data and the imprecision of many ecological models. As a first approach to this problem, we focus here on a simple system expressed as a discrete time model with 2-cycle behavior, reflecting alternating high and low population sizes. Such dynamics naturally arise in ecological systems with overcompensatory density dependence. We ask how the amount of detail included in the population estimates affects the ability to forecast the likelihood of changes in the phase of oscillation, meaning whether high populations occur in odd or in even years. We adjust the level of detail by converting continuous population levels to simple, coarse-grained descriptions using two-state and four-state models. We also consider a cubic noisy over-compensatory model with three parameters. The focus on phase changes is what distinguishes the question we are asking and the methods we use from more standard time series approaches. Obviously, adding observation states improves the ability to forecast phase shifts. In particular, the four-state model and cubic model outperform the two-state model because they include a transition state, through which the dynamics typically pass during a phase change. Nonetheless, at high noise levels the improvement in forecast skill is relatively modest. Additionally, the frequency of phase changes depends strongly on the noise level, and is much less affected by the parameter determining amplitude in the population model, so phase shift frequencies could possibly be used to infer noise levels.

Noise-induced versus intrinsic oscillation in ecological systems.

Studies of oscillatory populations have a long history in ecology. A first-principles understanding of these dynamics can provide insights into causes of population regulation and help with selecting detailed predictive models. A particularly difficult challenge is determining the relative role of deterministic versus stochastic forces in producing oscillations. We employ statistical physics concepts, including measures of spatial synchrony, that incorporate patterns at all scales and are novel to ecology, to show that spatial patterns can, under broad and well-defined circumstances, elucidate drivers of population dynamics. We find that when neighbours are coupled (e.g. by dispersal), noisy intrinsic oscillations become distinguishable from noise-induced oscillations at a transition point related to synchronisation that is distinct from the deterministic bifurcation point. We derive this transition point and show that it diverges from the deterministic bifurcation point as stochasticity increases. The concept of universality suggests that the results are robust and widely applicable.

Density dependent Resource Budget Model for alternate bearing.

Alternate bearing, seen in many types of plants, is the variable yield with a strongly biennial pattern. In this paper, we introduce a new model for alternate bearing behavior. Similar to the well-known Resource Budget Model, our model is based on the balance between photosynthesis or other limiting resource accumulation and reproduction processes. We consider two novel features with our model, 1) the existence of a finite capacity in the tree's resource reservoir and 2) the possibility of having low (but non-zero) yield when the tree's resource level is low. We achieve the former using a density dependent resource accumulation function, and the latter by removing the concept of the well-defined threshold used in the Resource Budget Model. At the level of an individual tree, our model has a stable two-cycle solution, which is suitable to model plants in which the alternate bearing behavior is pronounced. We incorporate environmental stochasticity by adding two uncorrelated noise terms to the parameters of the model associated with the nutrient accumulation and reproduction processes. Furthermore, we examine the model's behavior on a system of two coupled trees with direct coupling. Unlike the coupled Resource Budget Model, for which the only stable solution is the out-of-phase solution, our model with direct coupling has stable in-phase period-2 solutions. This suggests that our model might serve to explain spatial synchrony on a larger scale.

Dynamical Ising model of spatially coupled ecological oscillators.

Long-range synchrony from short-range interactions is a familiar pattern in biological and physical systems, many of which share a common set of 'universal' properties at the point of synchronization. Common biological systems of coupled oscillators have been shown to be members of the Ising universality class, meaning that the very simple Ising model replicates certain spatial statistics of these systems at stationarity. This observation is useful because it reveals which aspects of spatial pattern arise independently of the details governing local dynamics, resulting in both deeper understanding of and a simpler baseline model for biological synchrony. However, in many situations a system's dynamics are of greater interest than their static spatial properties. Here, we ask whether a dynamical Ising model can replicate universal and non-universal features of ecological systems, using noisy coupled metapopulation models with two-cycle dynamics as a case study. The standard Ising model makes unrealistic dynamical predictions, but the Ising model with memory corrects this by using an additional parameter to reflect the tendency for local dynamics to maintain their phase of oscillation. By fitting the two parameters of the Ising model with memory to simulated ecological dynamics, we assess the correspondence between the Ising and ecological models in several of their features (location of the critical boundary in parameter space between synchronous and asynchronous dynamics, probability of local phase changes and ability to predict future dynamics). We find that the Ising model with memory is reasonably good at representing these properties of ecological metapopulations. The correspondence between these models creates the potential for the simple and well-known Ising class of models to become a valuable tool for understanding complex biological systems.