A study of computational and conceptual complexities of compartment and agent based models

Prateek Kunwar; Oleksandr Markovichenko; Monique Chyba; Yuriy Mileyko; Alice Koniges; Thomas Lee

doi:10.3934/nhm.2022011

Article Contents

2022, Volume 17, Issue 3: 359-384. Doi: 10.3934/nhm.2022011

This issue Previous Article Mathematical analysis of a hybrid model: Impacts of individual behaviors on the spreading of an epidemic Next Article Vaccination strategies through intra—compartmental dynamics

A study of computational and conceptual complexities of compartment and agent based models

1.
Department of Mathematics, University of Hawai'i at Mānoa, Honolulu, HI 96822, USA
2.
Data Science Institute, University of Hawai'i at Mānoa, Honolulu, HI 96822, USA
3.
Office of Public Health Studies, University of Hawai'i at Mānoa, Honolulu, HI 96822, USA

^* Corresponding author: chyba@hawaii.edu
^* Corresponding author: chyba@hawaii.edu

Received: June 2021

Revised: November 2021

Early access: March 2022

Published: June 2022

The first five authors are supported by NSF grant No. 2030789

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Abstract

The ongoing COVID-19 pandemic highlights the essential role of mathematical models in understanding the spread of the virus along with a quantifiable and science-based prediction of the impact of various mitigation measures. Numerous types of models have been employed with various levels of success. This leads to the question of what kind of a mathematical model is most appropriate for a given situation. We consider two widely used types of models: equation-based models (such as standard compartmental epidemiological models) and agent-based models. We assess their performance by modeling the spread of COVID-19 on the Hawaiian island of Oahu under different scenarios. We show that when it comes to information crucial to decision making, both models produce very similar results. At the same time, the two types of models exhibit very different characteristics when considering their computational and conceptual complexity. Consequently, we conclude that choosing the model should be mostly guided by available computational and human resources.

Keywords:

SARS-CoV-2,
Epidemiological Modeling,
Agent-Based Model,
Compartmental Model,
Conceptual and Computational Complexity.

Mathematics Subject Classification: Primary: 92D30, 9208; Secondary: 68W01.

Citation:

FullText(HTML)

Figure 1. Basic SEIR Model diagram and parameters

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Figure 2. Diagram of our basic compartmental model

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Figure 3. Blue denotes the SEIR model fit for Honolulu county from March 6 to October 15, 2020. The dots represent the actual daily cases from the Hawai'i DOH dashboard [18]. In red are the optimized transmission rates $ \beta $ (aligned with non pharmaceutical mitigation measures that were taken by the State of Hawai'i)

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Figure 4. Sub-Diagram for travelers assumptions

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Figure 5. Diagram of our compartmental model with travelers

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Figure 6. Top: Honolulu County fit from March 6, 2020 including travelers from October 15 to December 27, 2020. Bottom: Honolulu County fit zoomed in for period of October 15 - December 27 with the value for the basal transmission rate

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Figure 7. Diagram of our compartmental model including vaccines

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Figure 8. Top: Honolulu County fit from March 6, 2020 including travelers starting October 15, 2020 and vaccination starting December 27, 2020. Simulation runs through April 25, 2021. Bottom: Zoomed in on the period where both vaccination and travelers are included with the corresponding basal transmission rates

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Figure 9. Sample contact network representing individuals in the population as nodes and the interactions for possible viral transmission among them as edges. The different colors refer to four different types of contacts or individuals in the population (LHS). The vaccinated individuals will have a reduced transmission which is reflected in their state (RHS)

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Figure 10. Diagram of basic Covasim simulation algorithm

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Figure 11. In green is the Covasim model fit for Honolulu county from March 6 to October 15, 2020. Included are the optimized transmission rates

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Figure 12. Top: Covasim fit for Honolulu county from March 6 to April 25, 2021 with travelers and vaccine included. Bottom: zoomed in on the period October 15, 2020 - April 25, 2021 including the corresponding transmission rates

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Figure 13. Increase in simulation time as a function of problem size for serial Covasim runs. For the top graph, we set the population size equal to $ 1 $ million and run 15 simulations for each scenario with a different number of days starting from 50 to 500. For the bottom graph one we set the number of days equal to 150 and run 15 simulations for each scenario with different population sizes, ranging from a thousand to a million, with one additional point for a population of size $ 50 $ million

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Figure 14. Increasing computational cost of the compartmental model. For each number of simulation days, an average of 15 simulations is taken

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Figure 15. Compartmental(blue) and Covasim (green) fit from March 6, 2020 to April 25, 2021 including travelers and vaccines

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Figure 16. SEIR (blue) and Covasim(green) benchmark scenarios forecasting spread and vaccination

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Figure 17. The mean of 20 covasim simulations (black) with simulations with highest (red), lowest (magenta), earliest (blue) and latest (green) peaks

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Table 1. SEIR basic model variables. Isolated accounts for quarantine and hospitalization

Description of the variables in the EBM model.
Variable		Description
$ S(t) $		Number of total susceptible individuals
$ E_{i}(t) $ (resp. $ E_{q, i}(t) $)		Number of asymptomatic infected individuals $ i $ days after exposure who are not quarantined (resp. qurantined)
$ I_{j}(t) $ (resp. $ I_{q, j}(t) $), $ i=0, 1 $		Number of symptomatic infected individuals $ i $ days after the onset of symptoms who are not isolated (resp. isolated)
$ I_{j}(t) $ (resp. $ I_{q, j}(t) $), $ j=3, 4, 5 $		Number of symptomatic infected individuals at the nominal stage $ i $ of the illness that has not been isolated (resp. isolated). Note that a person can stay at a given stage for several days
$ R(t) $		Number of removed (recovered or deceased) individuals

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Table 2. Parameters intrinsic to COVID-19

Parameter, meaning		Value
$ \beta $, basal transmission rates		optimized to fit data
Factors modifying transmission rate
$ \varepsilon $, asymptomatic transmission (25% reduction in transmission)		0.75
$ \rho $, reduced healthcare worker interactions		0.8
$ \gamma $, quarantine (80% reduction in transmission)		0.2
$ \kappa $, hospital precautions		0.5
$ \eta $, healthcare worker precautions		$ 0.2375 $
Population fractions
$ p_i $, $ i= 0, \ldots, 13$, onset of symptoms after day $ i $		0.000792, 0.00198, 0.1056, 0.198, 0.2376, 0.0858, 0.0528, 0.0462, 0.0396, 0.0264, 0.0198, 0.0198, 0.0198, 0
$ q_{s, i} $, $ i= 0, \ldots, 4$, symptomatic quarantine after day/stage $ i $		C: 0.1, 0.4, 0.8, 0.9, 0.99; H: 0.2, 0.5, 0.9, 0.98, 0.99
r, transition to next symptomatic day/stage		0.2
$ \nu $, symptomatic hospitalization		0.11

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Table 3. Parameters intrinsic to travelers

Parameter, meaning		Value
Factors modifying transmission rate
$ \rho_v $, reduced interaction of travelers with community		0.5
$ \phi_1 $, percentage of tested travelers		vary by destination (0.86 for Honolulu)
$ \phi_2 $, false negative test		0.005 (assuming Nucleic Acid Amplification Test)
$ \phi_3 $, prevalence		0.05
$ \phi_4 $, untested, exposed into quarantine		0.99

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Table 4. Traveler Data for Honolulu County

Dates	Average Tourists per day	Average Returning Residents per day
Oct 15 - Oct 28	1353	692
Oct 29 - Nov 11	2124	716
Nov 12 - Nov 25	3051	967
Nov 26 - Dec 9	2028	951
Dec 10 - Dec 23	4724	1014
Dec 24 - Jan 6	2195	1018
Jan 7 - Jan 20	1522	1053
Jan 21 - Feb 3	1531	710
Feb 4 - Feb 18	2828	843
Feb 19 - Mar 4	2832	942
Mar 5 - Mar 19	4483	1017
Mar 20 - Apr 5	6263	1543
Apr 6 - Apr 20	6231	1087
Apr 21 - Apr 25	5683	1331

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Table 5. Parameters intrinsic to vaccination used in our simulations

Parameter, meaning		Value
Factors modifying transmission rate
$ \mu_1 $, reduced susceptibility after Dose 1		1 (we assume no reduction in susceptibility after dose 1)
$ \mu_2 $, reduced susceptibility after Dose 2		1 (we assume no reduction in susceptibility after dose 2)
$ \psi $, fraction of newly fully vaccinated to dose 1 vaccinated		1/21
$ \omega $, reduced transmissibility due to vaccination		0.20
$ \bar{p}_i $, $ i=0, 1, ...13 $, probability of onset of symptoms after day i (after vaccination)		0.000492, 0.001080, 0.002056, 0.0415, 0.002376, 0.000858, 0.000528, 0.000302, 0.00019, 0.00019, 0.00019, 0.00019, 0.00019, 0
$ \theta $, proportion of travelers assumed to be unvaccinated		1
$ NV $, vaccinations received per day		2500

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