Effect of hot zone infection outbreaks on the dynamics of SARS-CoV-2 spread in the community at large (preprint)

Transmission of SARS-CoV-2 appears especially effective in "hot zone" locations where individuals interact in close proximity. We present mathematical models describing two types of hot zones. First, we consider a metapopulation model of infection spread where transmission hot zones are explicitly described by independent demes in which the same people repeatedly interact (referred to as "static" hot zones, e.g. nursing homes, food processing plants, prisons, etc.). These are assumed to exists in addition to a "community at large" compartment in which virus transmission is less effective. This model yields a number of predictions that are relevant to interpreting epidemiological patterns in COVID19 data. Even if the rate of community virus spread is assumed to be relatively slow, outbreaks in hot zones can temporarily accelerate initial community virus growth, which can lead to an overestimation of the viral reproduction number in the general population. Further, the model suggests that hot zones are a reservoir enabling the prolonged persistence of the virus at "infection plateaus" following implementation of non-pharmaceutical interventions, which has been frequently observed in data. The second model considers "dynamic" hot zones, which can repeatedly form by drawing random individuals from the community, and subsequently dissolve (e.g. restaurants, bars, movie theaters). While dynamic hot zones can accelerate the average rate of community virus spread and can provide opportunities for targeted interventions, they do not predict the occurrence of infection plateaus or other atypical epidemiological dynamics. The models therefore identify two types of transmission hot zones with very different effects on the infection dynamics, which warrants further epidemiological investigations.

Role of high-dose exposure in transmission hot zones as a driver of SARS-CoV2 dynamics (preprint)

Epidemiological data on the spread of SARS-CoV-2 in the absence and presence of various non-pharmaceutical interventions indicate that the virus is not transmitted uniformly in the population. Transmission tends to be more effective in select settings that involve exposure to relatively high viral dose, such as in crowded indoor settings, assisted living facilities, prisons, or food processing plants. To explore the effect on infection dynamics, we describe a new mathematical model where transmission can occur (i) in the community at large, characterized by low dose exposure and mostly mild disease, and (ii) in so called transmission hot zones, characterized by high dose exposure that can be associated with more severe disease. Interestingly, we find that successful infection spread can hinge upon high-dose hot zone transmission, yet the majority of infections are predicted to occur in the community at large with mild disease. This gives rise to the prediction that targeted interventions that specifically reduce virus transmission in the hot zones (but not in the community at large) have the potential to suppress overall infection spread, including in the community at large. The model can further reconcile seemingly contradicting epidemiological observations. While in some locations like California, strict stay-home orders failed to significantly reduce infection prevalence, in other locations, such as New York and several European countries, stay-home orders lead to a pronounced fall in infection levels, which remained suppressed for some months after re-opening of society. Differences in hot zone transmission levels during and after social distancing interventions can account for these diverging infection patterns. These modeling results warrant further epidemiological investigations into the role of high dose hot zone transmission for the maintenance of SARS-CoV-2 spread.

Modeling the dynamics of COVID19 spread during and after social distancing (preprint)

Non-pharmaceutical intervention measures, such as social distancing, have so far been the only means to slow the spread of COVID19. In the United States, strict social distancing has resulted in different types infection dynamics. In some states, such as New York, extensive infection spread was followed by a pronounced decline of infection levels. In other states, such as California, less infection spread occurred before strict social distancing, and a different pattern was observed. Instead of a pronounced infection decline, a long-lasting plateau is evident, characterized by similar daily new infection levels. While these plateau dynamics cannot be readily reproduced with standard SIR infection models, we show that network models, in which individuals and their social contacts are explicitly tracked, can reproduce the plateau if network connections are cut due to social distancing measures. The reason is that in networks characterized by a 2D spatial structure, infection tends to spread quadratically with time, but as edges are randomly removed, the infection spreads along nearly one-dimensional infection "corridors", resulting in plateau dynamics. Interestingly, the plateau dynamics are predicted to eventually transition into an infection decline phase without any further increase in social distancing measures. Additionally, the models suggest that a potential second wave becomes significantly less pronounced if social distancing is only relaxed once the dynamics have transitioned to the decline phase. The network models analyzed here allow us to interpret and reconcile different infection dynamics during social distancing observed in various US states.

Patterns of the COVID19 epidemic spread around the world: exponential vs power laws (preprint)

We have analyzed the COVID19 epidemic data of more than 174 countries (excluding China) in the period between January 22 and March 28, 2020. We found that some countries (such as the US, the UK, and Canada) follow an exponential epidemic growth, while others (like Italy and several other European countries) show a power law like growth. At the same time, regardless of the best fitting law, most countries can be shown to follow a trajectory similar to that of Italy, but with varying degrees of delay. We found that countries with ``younger" epidemics tend to exhibit more exponential like behavior, while countries that are closer behind Italy tend to follow a power law growth. We hypothesize that there is a universal growth pattern of this infection that starts off as exponential and subsequently becomes more power law like. Although it cannot be excluded that this growth pattern is a consequence of social distancing measures, an alternative explanation is that it is an intrinsic epidemic growth law, dictated by a spatially distributed community structure, where the growth in individual highly mixed communities is exponential but the longer term, local geographical spread (in the absence of global mixing) results in a power-law. This is supported by computer simulations of a metapopulation model that gives rise to predictions about the growth dynamics that are consistent with correlations found in the epidemiological data. Therefore, seeing a deviation from straight exponential growth may not be a consequence of working non-pharmaceutical interventions (except for, perhaps, restricting the air travel). Instead, this is a normal course of raging infection spread. On the practical side, this cautions us against overly optimistic interpretations of the countries epidemic development and emphasizes the need to continue improving the compliance with social distancing behavior recommendations.