These notes expand on the guide embedded in the game to: (1) describe the determination and usage of the main parameters, (2) outline some limitations, and (3) list down references.

Zones 1 to 5 essentially compose a difficulty ramp leading to Zones 6 and 7. The latter two hew closest to real-world data. Zone 8 leans more towards a subjective description of what the threat of COVID-19 is like in areas with hyper-concentrated density.

Parameters

The detailed parameters of Zones 2 to 8 can be seen in the Sandbox Editor in Zone 9.

Transmission Risk

"Transmission risk" is defined here as the probability of contracting the virus on contact with an infected person. "Contact" in turn is defined in [1] as a meeting involving face-to-face conversation or touch. The transmission risk in the real world is roughly estimated at 1% from [2] and [3]. To translate that into the game, the mean daily contacts in [1] (12.5 contacts per person per day) is divided by the mean daily contacts in Zones 6 and 7 (0.35 contacts per person per game day) multiplied by 1%. That's 12.5 / 0.35 x 1% ≈ 36% transmission risk. Seen another way, one contact event in Zones 6 and 7 is taken to represent ~36 real-world contacts.

Transmission Risk Modifiers

Masking in non-healthcare settings—where medical-grade masks are less common—is associated with an aggregated relative risk of 56% [4], translated in the game as reducing the transmission risk by 44%. Eye protection such as goggles and face shields are associated with an overall relative risk of 34% [4], interpreted in the game as reducing the transmission risk by 66%. Hand washing reduces risk of infection by 24% [5]. Social distancing of one to two meters is associated with an overall relative risk of 30% [4], implemented in the game as activating contact avoidance 70% of the time.

Disease Progression

The probabilities for progression from one state to the next is based on the case severity distribution in [6] with the proportion of asymptomatics checked with data from [7]. The various periods of the progression are based on [8], [9], and [10] as summarized in [11]. and supplemented by [12] for the estimated length of the critical period. The interpretation in the game is as follows: 81% of asymptomatics progress to symptomatic in two to 14 days. 17% of symptomatics progress to severe in five days. 29% of severe patients progress to critical in another five days. Finally, 49% of critical patients expire in eight days. Infected townsfolk who do not expire recover after 20 to 32 after contracting the virus.

Progression Modifiers

In the game, there are two sources of progression modifiers (or risk factors)—comorbidities (MCs) and age (MAs). The list of comorbidities, their respective case fatality rates (CFRs), and CFRs by age group are taken from [6] and buttressed by [13], [14], and [15].

MCs are factors that increase the probability of the disease worsening. To obtain those, the CFR of each comorbidty is dividied by the CFR for no underlying condition. The MCs are used in the following way. The probabilities of progression from symptomatic to severe, from severe to critical, and from critical to dead are each multiplied by the cube root of the MC relevant to a given individual. This is to distribute the MC across the three mentioned stages while keeping its overall effect. The prevalence of comorbidities are drawn from [16], [17], [18], [19], and [20] representing global figures that are then applied to the population in the game.

MAs either increase or decrease the probability of the disease worsening. Older individuals tend to have higher risk and younger individuals lower. To obtain the MAs, the CFR of each age bracket is divided by the CFR for 50-59 year olds. The MAs are then used in the same manner as the MCs above. The effect of MCs and MAs is cumulative.

Hospital Beds

The world has about three hospital beds per 1000 people [21]. Countries with a bed capacity of one per a hundred people are rare. ICU beds are even fewer (for instance in [22]). A possible justification for making more ICU beds available in the game is the recent ramping up of hospital resources. Still, the actual number of ICU beds is unlikely to reach one per 100 people for most communities.

Economy

The daily revenue from each townsfolk in the game adds up in one year to about 22% of the average annual salary in Cebu City, Philippines [23] where the game is being developed. This revenue can be treated as taxes paid by the townsfolk (as income tax, sales tax, and others). The initial funds for Zones 2 to 5 are about equal to each zone's respective income in six months before the pandemic; it's one-third of the expected income in the same period for Zones 6 to 8.

Each Coronavirus test kit in the game costs the town $37 (from [26]). The town spends a token $1 to administer a test. Isolating or quarantining an individual costs the town $8 a day, about equal to the minimum wage. Lastly, hospitalization for each COVID-19 patient costs the town $861—computed by taking the average of the compensation for severe pneumonia cases and critical cases in [28] divided by 13 days (the period of hospitalization in game time).

Limitations

Many aspects of the simulator can be improved. Some limitations then, in addition to those already identified, will be mentioned for future work.

The first is that human beings are not gas molecules that bounce around randomly. Humans too can exchange information such as to avoid certain areas with known incidence of infection.

The second is that basing the probabilities of disease progression on the severity distribution in [6] could be a crude estimate at best of the actual probabilities. Although the data in [6] consists of a large sample of more than 72,000 patient records from China that covers a period of about two months, it still remains the case that severity distribution is not exactly the same as disease progression. Moreover, many asymptomatic cases could have been undetected.

The third limitation I will point out is the oversimplification in the game's uniform risk of transmission throughout the period of infection when evidence points to viral load—and hence, transmission risk—peaking five to six days after the onset of symptoms then subsiding after [26].

Fourth, the porosity parameter, which corresponds to transmission from outside town, is implemented in quite a contrived manner. Setting the porosity to moderate in Sandbox Mode, for example, a new infection appears whenever the incidence drops to zero until the six-month limit is reached.​

Fifth, the comorbidities are distributed among the population regardless of age or sex.

Sixth, the comorbidities documented in [6], [13], and [15] were observed from Chinese patients which exclude a comorbidty frequently mentioned elsewehere (such as in [29]), namely, obesity.

Seventh, the CFRs of patients in [6], [13], [14], and [15] already account for comorbidities and age. Extracting progression modifiers from these studies may magnify the effect of comorbidites on CFRs. Although MAs may balance out the net effect as they point in opposite directions.

Eighth, a similar magnification of effects could also result from the transmission risk modifiers.

Despite the possible distortions in the previous two limitations, keeping the modifiers in the game is still considered valuable as they show, for example, how better hygiene can save lives as well as how those with pre-existing conditions or advanced age need extra protection. Caution is of course warranted in interpreting the numbers coming out of the game.

The ninth limitation is that the simulator does not have the equivalent of law enforcement. Townsfolk who refuse to comply with quarantine cannot be compelled to.

And tenth, the game economy can be fine-tuned in many places. For instance, everyone is considered able to generate income even those not of working age. Also, there is no mechanism for borrowing money. Still another is that tax collection occurs daily contrary to usual practice.

References

[1]       K. O. Kwok et al., "Temporal variation of human encounters and the number of locations in which they occur: a longitudinal study of Hong Kong residents," J. R. Soc. Interface, vol. 15, no. 20170838, Jan., 2018. doi: https://dx.doi.org/10.1098/rsif.2017.0838.

[2]       M. A. Otto, "COVID-19 update: Transmission 5% or less among close contacts," Hospitalist, Mar. 11, 2020. [Online]. Available: https://www.the-hospitalist.org/hospitalist/article/218769/coronavirus-updates/covid-19-update-transmission-5-or-less-among-close

[3]       H. Cheng at al., "Contact tracing assessment of COVID-19 transmission dynamics in Taiwan and risk at different exposure periods before and after symptom onset," JAMA Intern. Med., May, 2020. doi: https://dx.doi.org/10.1001/jamainternmed.2020.2020.

[4]       D. K. Chu et al., "Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: a systematic review and meta-analysis," Lancet, Jun., 2020. doi: https://dx.doi.org/10.1016/S0140-6736(20)31142-9.

[5]       T. Rabie and V. Curtis, "Handwashing and risk of respiratory infections: a quantitative systematic review," Trop. Med. Int. Health, Mar., 2006. doi: https://dx.doi.org/10.1111/j.1365-3156.2006.01568.x.

[6]       The Novel Coronavirus Pneumonia Emergency Response Epidemiology Team, "The epidemiological characteristics of an outbreak of 2019 novel coronavirus diseases (COVID-19)—China 2020," China CDC Weekly, vol. 2, no. 8, Feb., 2020. doi: https://dx.doi.org/10.46234/ccdcw2020.032.

[7]       M. Kenji et al., "Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship, Yokohama, Japan, 2020," Eurosurveill. 2020, vol. 25, no. 10, Mar. 12, 2020. doi: https://dx.doi.org/10.2807/1560-7917.ES.2020.25.10.2000180.

[8]       Center for Disease Control and Prevention, "Symptoms of Coronavirus," Center Disease Control Prevention, May, 2020. [Online]. Available: www.cdc.gov/coronavirus/2019-ncov/about/symptoms.html

[9]     D. Wang et al., "Clinical characteristics of 138 hospitalized patients with 2019 Novel Coronavirus–infected pneumonia in Wuhan, China," JAMA 2020, vol. 323, no. 11, Feb. 7, 2020. doi: https://dx.doi.org/10.1001/jama.2020.1585.

[10]     X. Jiang et al., "Towards an artificial intelligence framework for data-driven prediction of coronavirus clinical severity," Comp. Mat. Continua, vol. 63, no. 1, Mar. 30, 2020. doi: https://dx.doi.org/10.32604/cmc.2020.010691.

[11]     A. Bendix, "A day-by-day breakdown of coronavirus symptoms shows how the disease COVID-19 goes from bad to worse," Bus. Insider, Apr., 2020. [Online]. Available: https://www.businessinsider.com/coronavirus-covid19-day-by-day-symptoms-patients-2020-2

[12]     Health Information and Quality Authority, "Evidence summary for average length of stay in the intensive care unit for COVID-19," Health Inf. Qual. Authority, Smithfield, Dublin, 2020. Available: https://www.hiqa.ie/sites/default/files/2020-04/Evidence-summary_Covid-19_average-LOS-in-ICU.pdf

[13]     F. Caramelo et al., "Estimation of risk factors for COVID-19 mortality—preliminary results," medRxiv, Feb. 25, 2020. doi: https://dx.doi.org/10.1101/2020.02.24.20027268.

[14]     J. Oke and C. Heneghan, "Global Covid-19 Case Fatality Rates," Centre Evidence-Based Med., Jun., 2020. [Online]. Available: https://www.cebm.net/covid-19/global-covid-19-case-fatality-rates/

[15]     Center for Disease Control and Prevention, "Interim Clinical Guidance for Management of Patients with Confirmed Coronavirus Disease (COVID-19)," Center Disease Control Prevention, Jun., 2020. [Online]. Available: https://www.cdc.gov/coronavirus/2019-ncov/hcp/clinical-guidance-management-patients.html

[16]     G. A. Roth et al., "Global, regional, and national burden of cardiovascular diseases for 10 Causes, 1990 to 2015," J. Am. Col.l Cardiol., vol. 70, no. 1, Jul., 4, 2017. doi: https://dx.doi.org/10.1016/j.jacc.2017.04.052.

[17]     P. Saeedi et al., "Global and regional diabetes prevalence estimates for 2019 and projections for 2030 and 2045: Results from the International Diabetes Federation Diabetes Atlas, 9th edition," Diabetes Res. Clin. Pract., vol. 157, no. 107843, Nov. 1, 2019. doi: https://doi.org/10.1016/j.diabres.2019.107843.

[18]     M. Xie et al. "Trends in prevalence and incidence of chronic respiratory diseases from 1990 to 2017," Respiratory Res., vol. 21, no. 49, Feb. 11, 2020. doi: https://doi.org/10.1186/s12931-020-1291-8.

[19]     World Health Organization, "Hypertension," World Health Organization, Sept. 13, 2019. [Online]. Available: https://www.who.int/news-room/fact-sheets/detail/hypertension

[20]     F. Bray et al., " Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries," CA: Cancer J. Clinicians, vol. 68, no. 6, Sept. 12, 2018. doi: https://doi.org/10.3322/caac.21492.

[21]     The World Bank, "Hospital beds (per 1,000 people)," World Bank, 2020. [Online]. Available: https://data.worldbank.org/indicator/SH.MED.BEDS.ZS

[22]     UP COVID-19 Pandemic Response Team, "Estimating Local Healthcare Capacity to Deal with COVID-19 Case Surge: Analysis and Recommendations," University Philippines, Apr., 2020. [Online]. Available: https://www.up.edu.ph/estimating-local-healthcare-capacity-to-deal-with-covid-19-case-surge-analysis-and-recommendations/

[23]     PayScale, "Average Salary in Cebu City, Philippines ₱249k," PayScale, 2020. [Online]. Available: https://www.payscale.com/research/PH/Location=Cebu-City/Salary

[24]     National Wages and Productivity Commission, "Region VII (Central Visayas) Daily Minimum Wage Rates," Nat. Wages Productiv. Commission, 2019. [Online]. Available: https://nwpc.dole.gov.ph/regionandwages/region-vii-central-visayas/

[25]     Department of Finance National Tax Research Center, "Where Does Your Tax Money Go?," Dept. Finance Nat. Tax Res. Center, Jun., 2015. [Online]. Available: http://www.ntrc.gov.ph/images/Publications/where-does-your-tax-money-go.pdf

[26]     C. J. M. Gonzale, "UP NIH Spinoff begins mass distribution of DOST Pinoy-made COVID-19 test kits," Phil. Council Health Res. Develop., Apr., 2020. [Online]. Available: http://www.pchrd.dost.gov.ph/index.php/news/6537-up-nih-spinoff-begins-mass-distribution-of-dost-pinoy-made-covid-19-test-kits

[27]     PhilHealth, "PhilHealth guarantees continuing coverage for Covid-19 patients," PhilHealth, Apr., 2020. [Online]. Available: https://www.philhealth.gov.ph/news/2020/cont_coverage.php

[28]     A. Tamara and D. L. Tahapary, " Obesity as a predictor for a poor prognosis of COVID-19: A systematic review," Diabetes Metab. Syndr., Vol. 14, no. 4, July-August, 2020. doi: https://dx.doi.org/10.1016/j.dsx.2020.05.020.