Appendix A

A.1

This appendix includes a) details about the parameter settings for our simulator; b) simulator input data and related epidemic data resources; and c) our simulator source code and executed file, including detailed descriptions of parameter settings (i.e., external and estimated parameters).

Parameter Details

A.2

In this section, we thoroughly explain how we infer the parameters used in our model from R₀ derived by other system dynamics researchers. Then we list the value of environmental and epidemical parameters of our simulator by way of tables.

Parameters Inferred from Statistical Data

A.3

In previous projects that used the compartmental model to simulate a contagious disease (Koopman 2004; Lipsitch et al. 2003; Riley et al. 2003), these projects reduced R₀ to a simple relational expression A.1 (Anderson and May 1982; Becker 1992). In a situation where all of an infected individual's neighbors are susceptible, R₀ = contact rate _ transmission probability _ duration of infection.

(A.1)

A.4

After combining mirror identities with cellular automata, we modified the original expression A.1 to obtain another expression A.2.

(A.2)

where C_rate represents the rate of contact between an individual and his or her respective neighbors, C_time the number of contacts between the individual and those neighbors in one day, T_rate the average infected individual transmission rate, T_period the average infected individual transmission period, Avg. Mirror Identities the average number of mirror identities, and Num. of Neighbors the number of neighbors for each mirror identity.

A.5

Since we adopted the first layer of a Moore neighborhood for our simulation model, our C_rate = 1/8 and Num. of Neighbors = 8. In addition to adopting R₀ and transmission periods from epidemiologists, we adopted the average number of mirror identities and numbers of neighbors from sociologists, and then integrated R₀-derived parameters to simulate a contagious disease and derive a transmission rate.

A.6

R₀ is an epidemiological parameter derived from a system dynamics model. According to Lipsitch et al. (2003), Riley et al. (2003), Sebastian and Hoffmann (2003), and World Health Organization (2003), the SARS R₀ fluctuated between 2.6 and 3.0 persons. Based on statistical data from national and municipal health authorities, we know that the average transmissible period (T_period) was between 4.5 and 6 days. We adopted the following values from sociologists: Avg. Mirror Identities = 3 and Num. of Neighbors = 8. After calculating these values, expression A.2 can be used to derive the T_rate. A list of parameters used in our experiments is presented in Table A.1.

Table A.1: Parameters used in the experiments
	R0	Crate	Ctime	Trate	Tperiod	Avg. Mirror Identities	Num. of Neighbors
Singapore Taipei Toronto	2.7	1/8	4	0.045	5	3	8

A.7

We used Num. of Neighbors and Avg. Mirror Identities to build a two-dimensional simulator environment. C_time, C_rate, and T_period were used to determine individual transmission dynamics. R₀ was used to derive the T_rate, which was then used to determine individual transmission dynamics.

A.8

To validate our proposed model, we attempted to replicate an important R₀ property: when R₀ > 1, a disease is considered epidemic; when R₀ = 1, the disease is described as endemic; when R₀ < 1, the disease is easily suppressed. We believe that deconstructing R₀ makes it possible to choose an effective suite of simulation parameters once epidemiologists determine a transmissible period value. Since parameter sensitivity to an epidemic model varies, R₀ properties can be used to identify appropriate suites. In Figure A.1, the R₀ properties are identifiable when T_period = 6, Avg. Mirror Identities = 3, and C_time = 4. We divided our R₀ into the six parameters that we used to build our model for performing a contagious disease simulation. We believe our model can also be used to display the epidemiological properties of R₀.

Figure A.1. Epidemic curves (R0 = 1.4, 1.0, and 0.6) when Tperiod = 6, Avg. Mirror Identities = 3, and Ctime = 4

Initial Global Environment Parameters

Table A.2: Initial Global Environment Parameters
Attribute	Value	Description
P	100,000	Total number of agents.
M	5	Upper limit of an agent's mirror identities.
H	500	Height of the two-dimensional lattice used in the cellular automata.
W	500	Width of the two-dimensional lattice used in the cellular automata.
Avg. Mirror Identities	3 ~ 4	Average number of mirror identity.
DayIncubation	5	Average number of incubation days.
DayInfectious	25	Average number of infectious days.
DayRecovered	7	Average number of recovered days.
RateSuper	0.0001	Percentage of super-spreaders among total population.
RateYoung	0.3	Percentage of young (0 to 20 years) agents in total population.
RatePrime	0.5	Percentage of prime (21 to 60 years) agents in total population.
RateOld	0.2	Percentage of old (60 years and above) agents in total population.
RateInfection	0.045	Average infection rate.
RateDeath	0.204	Average death rate.

Input Epidemic Data And Related Resources

Singapore Simulation Input Data

Table A.3: Singapore Simulation Input Data
Time Step	Action	Persons	State	Public Health Policy	Special Description on the Simulator
2003/3/1	Trigger	1	Infectious		Super-spreader
2	Trigger	2	Infectious
11	Set			Reducing Public Contact	Efficacy = 0.9, Popularity = 0.5
15	Trigger	1	Incubation	Wearing Mask Policy for Healthcare Worker	Efficacy = 0.9, Popularity = 0.9
22	Trigger	2	Incubation
23	Set			Home Quarantines	10 days, Popularity = 0.9
				Controlling Hospital Access	Efficacy = 0.9, Popularity = 0.9
				Wearing Mask Policy for General Public	Efficacy = 0.9, Popularity = 0.5
25	Trigger	2	Infectious
52	Set			Taking Body Temperature	Efficacy = 0.9, Popularity = 0.5

A.9

The efficacy level of each policy was set at 0.9. Popularity level was set at 0.9 for policies that were strictly enforced by government health authorities and at 0.5 for policies whose success depended on the cooperation of the general public without strict enforcement.

Taipei Simulation Input Data

We used what we learned from our Singapore experiment to simulate the spread of the SARS virus in Taipei. We used only those imported cases and health policies announced by the Taipei Municipal Department of Health.

Table A.4: Taipei Simulation Input Data
Time Step	Action	Persons	State	Public Health Policy	Special Description on the Simulator
2003/3/20	Trigger	1	Infectious
2	Trigger	4	Incubation
9	Trigger	1	Incubation
11	Trigger	2	Infectious
12	Trigger	2	Infectious	Home Quarantines	10 days, Popularity = 0.9
14	Trigger	1	Infectious
27	Trigger	1	Infectious	Wearing Mask Policy for Healthcare Worker	Efficacy = 0.9, Popularity = 0.9
47	Set			Controlling Hospital Access	Efficacy = 0.9, Popularity = 0.9
53	Set			Home Quarantines	14 days, Popularity = 0.9
				Wearing Mask Policy for General Public	Efficacy = 0.9, Popularity = 0.5
74	Set			Home Quarantines	10 days, popularity = 0.9
88	Set			Taking Body Temperature	Efficacy = 0.9, Popularity = 0.5

Toronto Simulation Input Data

Table A.5: Toronto Simulation Input Data
Time Step	Action	Persons	State	Public Health Policy	Special Description on the Simulator
2003/2/23	Trigger	1	Infectious
6	Trigger	1	Infectious
19	Trigger	1	Infectious	Wearing Mask Policy for Healthcare Worker	Efficacy = 0.9, Popularity = 0.9
				Reducing Public Contact	Efficacy = 0.9, Popularity = 0.5
30	Trigger	1	Infectious
37	Set			Controlling Hospital Access	Efficacy = 0.9, Popularity = 0.9
				Home Quarantines	10 days, Popularity = 0.9
38	Trigger	1	Infectious
68	Close			All Public Health Policies opened before
91	Set			Wearing Mask Policy for Healthcare Worker	Efficacy = 0.9, Popularity = 0.9
112	Set			All Public Health Policies closed before

Related Epidemic Information Links

Singapore

• Singapore Government SARS Website:http://www.sars.gov.sg/index.html.
• Singapore Ministry of Health (MOH) SARS Website: http://www.moh.gov.sg/corp/sars/index.html.

Taipei

• Republic of China Department of Health SARS Online Information Center: http://www.doh.gov.tw/newverprog/proclaim/sars_list.asp.
• Center for Disease Control, Republic of China:http://www.cdc.gov.tw/sars/.
• Taipei Municipal Department of Health:http://sars.health.gov.tw/.

Toronto

• Health Canada: http://www.hcsc.gc.ca/english/protection/warnings/sars/index.html.
• SARS Timeline in Canada: http://www.mapleleafweb.com/education/spotlight/issue_31/timeline.html or http://www.ctv.ca/generic/WebSpecials/sars/timeline/timeline_sars.html.
• Toronto Public Health: http://www.toronto.ca/health/sars/index.htm.

WHO (World Health Organization)

• http://www.who.int/csr/sars/en/.

CDC (Centers of Disease control and Prevention)

• CDC SARS homepage: http://www.cdc.gov/ncidod/sars/.
• CDC Weekly Morbidity and Mortality Report (MMWR): http://www.cdc.gov/mmwr/.

Simulator Source Code And Simulator File

A.10

Please send requests for our source code and simulator to gis89802@cis.nctu.edu.tw or gis91572@cis.nctu.edu.tw.

References

ANDERSON R M and May R M (1982) Directly transmitted infectious diseases: control by vaccination. Science 215(4536), pp. 1053-1060.

BECKER N G (1992) Infectious-Diseases of Humans - Dynamics and Control. Australian Journal of Public Health, 16, pp. 208-209.

KOOPMAN J (2004) Modeling infection transmission. Annual Review of Public Health 25: 303-26.

RILEY S, Fraser C, Donnelly C A, Ghani A C, Abu-Raddad L J, Hedley A J, Leung G M, Ho L M, Lam T H, Thach T Q, Chau P, Chan K P, Lo S V, Leung P Y, Tsang T, Ho W, Lee K H, Lau E M, Ferguson N M, and Anderson R M (2003) Transmission Dynamics of the Etiological Agent of SARS in Hong Kong: Impact of Public Health Interventions. Science, 300(5627), pp. 1961-1966.

LIPSITCH M, Cohen T, Cooper B, Robins J M, Ma S, James L, Gopalakrishna G, Chew S K, Tan C C, Samore M H, Fisman D, and Murray M (2003) Transmission Dynamics and Control of Severe Acute Respiratory Syndrome. Science, 300(5627), pp. 1966-1970.

SEBASTIAN B and Hoffmann C (2003) SARS Reference. Flying Publisher.

WHO (WORLD HEALTH ORGANIZATION) (2003) Consensus document on the epidemiology of severe acute respiratory syndrome (SARS), http://www.who.int/csr/sars/en/WHOconsensus.pdf.

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© Copyright Journal of Artificial Societies and Social Simulation, [2004]