### Mathematical Biosciences and Engineering

2019, Issue 5: 4250-4273. doi: 10.3934/mbe.2019212
Research article Special Issues

# Comparative analysis of phenomenological growth models applied to epidemic outbreaks

• Received: 19 March 2019 Accepted: 12 May 2019 Published: 16 May 2019
• Phenomenological models are particularly useful for characterizing epidemic trajectories because they often offer a simple mathematical form defined through ordinary differential equations (ODEs) that in many cases can be solved explicitly. Such models avoid the description of biological mechanisms that may be difficult to identify, are based on a small number of model parameters that can be calibrated easily, and can be utilized for efficient and rapid forecasts with quantified uncertainty. These advantages motivate an in-depth examination of 37 data sets of epidemic outbreaks, with the aim to identify for each case the best suited model to describe epidemiological growth. Four parametric ODE-based models are chosen for study, namely the logistic and Gompertz model with their respective generalizations that in each case consists in elevating the cumulative incidence function to a power $p\in [0, 1]$. This parameter within the generalized models provides a criterion on the early growth behavior of the epidemic between constant incidence for $p = 0$, sub-exponential growth for $0 < p < 1$ and exponential growth for $p = 1$. Our systematic comparison of a number of epidemic outbreaks using phenomenological growth models indicates that the GLM model outperformed the other models in describing the great majority of the epidemic trajectories. In contrast, the errors of the GoM and GGoM models stay fairly close to each other and the contribution of the adjustment of $p$ remains subtle in some cases. More generally, we also discuss how this methodology could be extended to assess the "distance" between models irrespective of their complexity.

Citation: Raimund Bürger, Gerardo Chowell, Leidy Yissedt Lara-Díıaz. Comparative analysis of phenomenological growth models applied to epidemic outbreaks[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4250-4273. doi: 10.3934/mbe.2019212

### Related Papers:

• Phenomenological models are particularly useful for characterizing epidemic trajectories because they often offer a simple mathematical form defined through ordinary differential equations (ODEs) that in many cases can be solved explicitly. Such models avoid the description of biological mechanisms that may be difficult to identify, are based on a small number of model parameters that can be calibrated easily, and can be utilized for efficient and rapid forecasts with quantified uncertainty. These advantages motivate an in-depth examination of 37 data sets of epidemic outbreaks, with the aim to identify for each case the best suited model to describe epidemiological growth. Four parametric ODE-based models are chosen for study, namely the logistic and Gompertz model with their respective generalizations that in each case consists in elevating the cumulative incidence function to a power $p\in [0, 1]$. This parameter within the generalized models provides a criterion on the early growth behavior of the epidemic between constant incidence for $p = 0$, sub-exponential growth for $0 < p < 1$ and exponential growth for $p = 1$. Our systematic comparison of a number of epidemic outbreaks using phenomenological growth models indicates that the GLM model outperformed the other models in describing the great majority of the epidemic trajectories. In contrast, the errors of the GoM and GGoM models stay fairly close to each other and the contribution of the adjustment of $p$ remains subtle in some cases. More generally, we also discuss how this methodology could be extended to assess the "distance" between models irrespective of their complexity.

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