Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches

It is known that the parameters in the deterministic and stochastic SEIR epidemic models are structurally identifiable. For example, from knowledge of the infected population time series I(t) during the entire epidemic, the parameters can be successfully estimated. In this article we observe that estimation will fail in practice if only infected case data during the early part of the epidemic (pre-peak) is available. This fact can be explained using a long-known phenomenon called dynamical compensation. We use this concept to derive an unidentifiability manifold in the parameter space of SEIR that consists of parameters indistin-guishable to I(t) early in the epidemic. Thus, identifiability depends on the extent of the system trajectory that is available for observation. Although the existence of the unidentifiability manifold obstructs the ability to exactly determine the parameters, we suggest that it may be useful for uncertainty quantification purposes. A variant of SEIR recently proposed for COVID-19 modeling is also analyzed, and an analogous unidentifiability surface is derived.

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“…Then for all α , β , γ satisfying (10), the set by the quadratic equation (8). This agrees withİ, verifying the second differential equation.…”

Section: Identifiability In Linear Systemssupporting

confidence: 78%

Identifiability of infection model parameters early in an epidemic

Sauer

Berry

Ebeigbe

et al. 2020

Preprint

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“…However, one of the input variables for the Binomial distribution ̃( , ) ⋅ ( ) or ( , ) ⋅ ( ) was modeled with a continuous variable in our approach. We used the gamma distribution, matching the first two moments to obtain the transformation of the discrete Binomial distribution to its continuous approximation [16]. We avoided joint estimation of all parameters { Σ , , } due to heterogeneity in the aggregated data-a similar issue is discussed in [10].…”

Section: Statistical Inferencementioning

confidence: 99%

Real-Time Estimation of the Risk of Death from Novel Coronavirus (COVID-19) Infection: Inference Using Exported Cases

Jung

Akhmetzhanov

Hayashi

et al. 2020

Preprint

186

189

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The exported cases of 2019 novel coronavirus infection that were confirmed outside of China provide an opportunity to estimate the cumulative incidence and confirmed case fatality risk (cCFR) in mainland China. Knowledge of the cCFR is critical to characterize the severity and understand the pandemic potential of COVID-19 in the early stage of the epidemic. Using the exponential growth rate of the incidence, the present study statistically estimated the cCFR and the basic reproduction number-the average number of secondary cases generated by a single primary case in a naïve population. We modeled epidemic growth either from a single index case with illness onset on 8 December, 2019 (Scenario 1), or using the growth rate fitted along with the other parameters (Scenario 2) based on data from 20 exported cases reported by 24 January, 2020. The cumulative incidence in China by 24 January was estimated at 6924 cases (95% CI: 4885, 9211) and 19,289 cases (95% CI: 10,901, 30,158), respectively. The latest estimated values of the cCFR were 5.3% (95% CI: 3.5%, 7.5%) for Scenario 1 and 8.4% (95% CI: 5.3%, 12.3%) for Scenario 2. The basic reproduction number was estimated to be 2.1 (95% CI: 2.0, 2.2) and 3.2 (95% CI: 2.7, 3.7) for Scenarios 1 and 2, respectively. Based on these results, we argued that the current COVID-19 epidemic has a substantial potential for causing a pandemic. The proposed approach provides insights in early risk assessment using publicly available data.

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“…However, one of the input variables for the Binomial distribution u(r, θ e ) · I(t) or u(r, θ d ) · I(t) was modeled with a continuous variable in our approach. We used the gamma distribution, matching the first two moments to obtain the transformation of the discrete Binomial distribution to its continuous approximation [15,16]. We avoided joint estimation of all parameters {θ Σ , θ e , θ d } due to heterogeneity in the aggregated data-a similar issue is discussed in [10].…”

Section: Statistical Inferencementioning

confidence: 99%

Real-Time Estimation of the Risk of Death from Novel Coronavirus (COVID-19) Infection: Inference Using Exported Cases

Jung

Akhmetzhanov

Hayashi

et al. 2020

JCM

346

152

View full text Add to dashboard Cite

The exported cases of 2019 novel coronavirus infection that were confirmed outside China provide an opportunity to estimate the cumulative incidence and confirmed case fatality risk (cCFR) in mainland China. Knowledge of the cCFR is critical to characterize the severity and understand the pandemic potential of COVID-19 in the early stage of the epidemic. Using the exponential growth rate of the incidence, the present study statistically estimated the cCFR and the basic reproduction number-the average number of secondary cases generated by a single primary case in a naïve population. We modeled epidemic growth either from a single index case with illness onset on 8 December 2019 (Scenario 1), or using the growth rate fitted along with the other parameters (Scenario 2) based on data from 20 exported cases reported by 24 January 2020. The cumulative incidence in China by 24 January was estimated at 6924 cases (95% confidence interval [CI]: 4885, 9211) and 19,289 cases (95% CI: 10,901, 30,158), respectively. The latest estimated values of the cCFR were 5.3% (95% CI: 3.5%, 7.5%) for Scenario 1 and 8.4% (95% CI: 5.3%, 12.3%) for Scenario 2. The basic reproduction number was estimated to be 2.1 (95% CI: 2.0, 2.2) and 3.2 (95% CI: 2.7, 3.7) for Scenarios 1 and 2, respectively. Based on these results, we argued that the current COVID-19 epidemic has a substantial potential for causing a pandemic. The proposed approach provides insights in early risk assessment using publicly available data.

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Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches

Cited by 34 publications

References 24 publications

Identifiability of infection model parameters early in an epidemic

Identifiability of infection model parameters early in an epidemic

Real-Time Estimation of the Risk of Death from Novel Coronavirus (COVID-19) Infection: Inference Using Exported Cases

Real-Time Estimation of the Risk of Death from Novel Coronavirus (COVID-19) Infection: Inference Using Exported Cases

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