A Data-Informed Approach for Analysis, Validation, and Identification of COVID-19 Models

Abstract

The COVID-19 pandemic has generated an enormous amount of data, providing a unique opportunity for modeling and analysis. In this paper, we present a data-informed approach for building stochastic compartmental models that is grounded in the Markovian processes underlying these models. Our initial data analyses reveal that the SIRD model -- susceptiple (S), infected (I), recovered (R), and death (D) -- is not consistent with the data. In particular, the transition times expressed in the dataset do not obey exponential distributions, implying that there exist unmodeled (hidden) states. We make use of the available epidemiological data to inform the location of these hidden states, allowing us to develop an augmented compartmental model which includes states for hospitalization (H) and end of infectious viral shedding (V). Using the proposed model, we characterize delay distributions analytically and match model parameters to empirical quantities in the data to obtain a good model fit. Insights from an epidemiological perspective are presented, as well as their implications for mitigation and control strategies.

Using Timeliness in Tracking Infections

“…In the literature, in order to model epidemics, population is partitioned into groups called compartments. One such example is the SIR model used in [106] with the compartments susceptible (S), infected (I), and recovered (R) which has been further developed by adding states hospitalized (H), and death (D) in [107]. In these epidemic models, the transitions between the compartments are assumed to be Markovian.…”

“…In these epidemic models, the transitions between the compartments are assumed to be Markovian. In [107], with the epidemiological data, the delay distributions for the infected (I) to hospitalized (H), and infected (I) to death (D) are well approximated by exponential and gamma distributions, respectively. However, due to the lack of data availability the delay distribution for infected (I) to recovered (R) is modeled with gamma distribution with higher tolerance.…”

“…In our work, we modeled infection and recovery times, i.e., the delays between recovered (R) to infected (I) and infected (I) to recovered (R) with exponential distributions. Therefore, more realistic infection tracking models can be developed by considering gamma distributions as observed in [107]. This more realistic model corresponds to the problem of real-time timely tracking of a binary Markov source in a serially connected network.…”

Spatio-temporal modeling of COVID-19 epidemic

“…In actual conditions a disease process is more complicated and can consist of at least two stages: incubation (an infected person is not a source of contagion during a part of this period and has no apparent clinical signs of a disease) and a disease itself. SEIR model (Susceptible-Exposed-Infected-Removed model) allows taking incubation into account [9,10,17,20]. Three states considered within the SIR model are added with one more state, Exposed or infected in their incubation period.…”