Modeling between-population variation in COVID-19 dynamics in Hubei, Lombardy, and New York City

Abstract

As the COVID-19 pandemic continues, formulating targeted policy interventions that are informed by differential severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission dynamics will be of vital importance to national and regional governments. We develop an individual-level model for SARS-CoV-2 transmission that accounts for location-dependent distributions of age, household structure, and comorbidities. We use these distributions together with age-stratified contact matrices to instantiate specific models for Hubei, China; Lombardy, Italy; and New York City, United States. Using data on reported deaths to obtain a posterior distribution over unknown parameters, we infer differences in the progression of the epidemic in the three locations. We also examine the role of transmission due to particular age groups on total infections and deaths. The effect of limiting contacts by a particular age group varies by location, indicating that strategies to reduce transmission should be tailored based on population-specific demography and social structure. These findings highlight the role of between-population variation in formulating policy interventions. Across the three populations, though, we find that targeted "salutary sheltering" by 50% of a single age group may substantially curtail transmission when combined with the adoption of physical distancing measures by the rest of the population.

Keywords: COVID-19; SARS-CoV-2; modeling; nonpharmaceutical intervention.

Fig. 1.

We use a modified SEIR model, where the infectious states are subdivided into levels of disease severity. The transitions are probabilistic and there is a time lag for transitioning between states. For example, the magnified section shows the details of transitions between mild, recovered, and severe states. Each arrow consists of the probability of transition [e.g., $p_{m\to s}\left(a_i,c_i\right)$ denotes the probability of progressing from mild to severe] as well as the associated time lag (e.g., the time $t$ for progression from mild to severe is drawn from an exponential distribution with mean ${\lambda }_{m\to s}$). $a_i$ and $c_i$ denote the age and set of comorbidities for the infected individual $i$.

Fig. 2.

Posterior distribution over the number of deaths each day compared to the number of reported deaths. Light blue lines are individual samples from the posterior, green is the median, and the black dots are the number of reported deaths. The red dashed line represents the start of modeled contact reductions in each location.

Fig. 3.

Posterior distribution over $r_0$ and the fraction of infections documented in each location (Top) conditioning on reported deaths and (Bottom) conditioning on deaths in New York City and Lombardy being twice what was reported.

Fig. 4.

Number of new infections and new deaths in second-wave outbreak scenarios for each location. Each column shows a different level of physical distancing by the population as a whole, where contacts between all age groups are reduced to the given percentage of their starting value. The $x$ axis within each plot shows the result when the given fraction of a single age group shelters at home (in addition to physical distancing by the rest of the population). The result of this combination of sheltering and distancing is represented by a bar, where the color of the bar indicates the age group which engaged in sheltering (see key). The height of the bar gives the total number of infections or deaths in the population in that scenario. Each row gives the results for a single location, where the first two plots show the fraction of the population which is newly infected in the second wave and the next two plots show the number of new deaths which occur.