Evaluations of heterogeneous epidemic models with exponential and non-exponential distributions for latent period: the Case of COVID-19

Huiping Zang; Shengqiang Liu; Yi Lin; Huiping Zang; Shengqiang Liu; Yi Lin

doi:10.3934/mbe.2023560

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12579-12598. doi: 10.3934/mbe.2023560

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Evaluations of heterogeneous epidemic models with exponential and non-exponential distributions for latent period: the Case of COVID-19

School of Mathematical Sciences, Tiangong University, Tianjin 300387, China

Academic Editor: Xiang-Sheng Wang

Received: 16 March 2023 Revised: 30 April 2023 Accepted: 11 May 2023 Published: 26 May 2023

Most of heterogeneous epidemic models assume exponentially distributed sojourn times in infectious states, which may not be practical in reality and could affect the dynamics of the epidemic. This paper investigates the potential discrepancies between exponential and non-exponential distribution models in analyzing the transmission patterns of infectious diseases and evaluating control measures. Two SEIHR models with multiple subgroups based on different assumptions for latency are established: Model Ⅰ assumes an exponential distribution of latency, while Model Ⅱ assumes a gamma distribution. To overcome the challenges associated with the high dimensionality of GDM, we derive the basic reproduction number ($ R_{0} $) of the model theoretically, and apply numerical simulations to evaluate the effect of different interventions on EDM and GDM. Our results show that considering a more realistic gamma distribution of latency can change the peak numbers of infected and the timescales of an epidemic, and GDM may underestimate the infection eradication time and overestimate the peak value compared to EDM. Additionally, the two models can produce inconsistent predictions in estimating the time to reach the peak. Our study contributes to a more accurate understanding of disease transmission patterns, which is crucial for effective disease control and prevention.
- heterogeneous epidemic models,
- exponential distribution,
- gamma distribution,
- latent,
- numerical simulations
Citation: Huiping Zang, Shengqiang Liu, Yi Lin. Evaluations of heterogeneous epidemic models with exponential and non-exponential distributions for latent period: the Case of COVID-19[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12579-12598. doi: 10.3934/mbe.2023560

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Abstract

Most of heterogeneous epidemic models assume exponentially distributed sojourn times in infectious states, which may not be practical in reality and could affect the dynamics of the epidemic. This paper investigates the potential discrepancies between exponential and non-exponential distribution models in analyzing the transmission patterns of infectious diseases and evaluating control measures. Two SEIHR models with multiple subgroups based on different assumptions for latency are established: Model Ⅰ assumes an exponential distribution of latency, while Model Ⅱ assumes a gamma distribution. To overcome the challenges associated with the high dimensionality of GDM, we derive the basic reproduction number ($ R_{0} $) of the model theoretically, and apply numerical simulations to evaluate the effect of different interventions on EDM and GDM. Our results show that considering a more realistic gamma distribution of latency can change the peak numbers of infected and the timescales of an epidemic, and GDM may underestimate the infection eradication time and overestimate the peak value compared to EDM. Additionally, the two models can produce inconsistent predictions in estimating the time to reach the peak. Our study contributes to a more accurate understanding of disease transmission patterns, which is crucial for effective disease control and prevention.

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