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{"sheet":"Contents","index":0,"n_rows":14,"n_cols":3,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
[]
[null,null,"Copyright © 2020 Society of Actuaries"]
[]
[]
[]
[]
[null,"A Model of the Impact of Social Distancing on the Spread of a Communicable Virus"]
[]
[null,"This spreadsheet contains a simple model that demonstrates how social distancing could decelerate the transmission of a communicable virus."]
[null,"This is a stylized model that is intended solely for illustrative purposes.  This is not a \"real\" model based on COVID-19 data or data for any other virus."]
[null,"The model's default assumptions are not intended to reflect actual, real-world rates of transmission or lethality. Rather, the assumptions were invented for illustrative purposes."]
[null,"Note that the model is deterministic rather than stochastic."]
[]
[null,"Note that you must press \"Enable Content\" when this model opens. Otherwise, the VBA code that underpins the model will not be able to run."]

{"sheet":"Model","index":1,"n_rows":247,"n_cols":21,"rows_kept":247,"cut":false,"hidden":false,"merged":[[9,1,9,2],[9,3,9,4],[9,5,9,6]]}
[null,"Susceptible, Infected, Recovered (\"SIR\") Model of an Epidemic"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,100," Zoom Percent"]
[]
[]
[null,200,"Days per simulation",null,null,null,null,null,null,null,null,null,null,null,null,null,"Results at End of Simulation Horizon"]
[null,1,"Produce output every N days",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Case 1","Case 2","Case 3"]
[null,1,"On graph: 1 = total population, 2 = young population, 3 = old population",null,null,null,null,null,null,null,null,null,null,null,null,null,"Recovered",0.91293060779571533,0.85863626003265381,0.64723950624465942]
[null,0.5,"On graph: maximum y-axis value to display",null,null,null,null,null,null,null,null,null,null,null,null,null,"Susceptible",7.784590870141983E-2,0.1326616108417511,0.34165936708450317]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Infected",1.9032354430237319E-6,2.917244091804605E-5,4.5632366091012955E-3]
[null,"Case 1",null,"Case 2",null,"Case 3",null,null,null,null,null,null,null,null,null,null,"Deceased",9.2215230688452721E-3,8.6730914190411568E-3,6.5377764403820038E-3]
[null,"Low Risk","High Risk","Low Risk","High Risk","Low Risk","High Risk",null,null,null,null,null,null,null,null,null,"Table reflects the population selected in cell B7"]
[null,1,null,1,null,1,null,"At time zero: distribution of population (low risk + high risk = 100%)"]
[null,1000,null,1000,null,1000,null,"At time zero: number of persons infected out of 1 million"]
[null,0.01,null,0.01,null,0.01,null,"Probability of catching the virus if an uninfected person comes into contact with an infected person"]
[null,10,null,10,null,10,null,"Average duration of infection, in days"]
[null,0.01,null,0.01,null,0.01,null,"Probability that infection ends in death"]
[null,30,null,30,null,30,null,"Average number of person-to-person contacts each day: without social distancing adjustments"]
[null,10,null,10,null,10,null,"Average number of person-to-person contacts each day: with social distancing adjustments"]
[null,999,null,40,null,40,null,"Number of days (since time zero) until action is taken via the social distancing parameters shown on line 18"]
[null,20,null,10,null,60,null,"Total number of days during which social distancing policy will be enforced (after which we return to the social distancing parameters on row 17)"]
[null,3,null,3,null,3,null,"R-naught without social distancing (this is a model output rather than an input)"]
[null,1,null,1,null,1,null,"R-naught with with social distancing (this is a model output rather than an input)"]
[]
[null,"Simulation Results",null,null,null,null,null,null,null,"Recovered","Susceptible","Infected","Deceased"]
[]
[]
[null,"CASE 1",null,null,null,null,null,null,"CASE 2",null,null,null,null,null,null,"CASE 3"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,"Newly",null,null,null,null,null,null,"Newly",null,null,null,null,null,null,"Newly"]
[null,null,"Infected","Suscept","Recov","Deceased","Infected",null,null,"Infected","Suscept","Recov","Deceased","Infected",null,null,"Infected","Suscept","Recov","Deceased","Infected"]
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{"sheet":"The Model's Calculation Approac","index":2,"n_rows":14,"n_cols":2,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
[null,"The Model's Calculation Approach"]
[]
[null,"The model permits a user to divide a population into \"low risk\" and \"high risk\" subgroups, and it assumes that these two groups intermingle at random. "]
[null,"Suppose that the low risk group is 90% of the population, while the high risk group is 10%. In this case, any social encounter between two individuals will "]
[null,"have an 81% of involving 2 low risk individuals, a 1% chance of involving 2 high risk individuals, and an 18% chance of involving 1 low risk and 1 high risk"]
[null,"individual. If you wish, you may place the entire population into a single risk group as opposed to two groups. To do this, just leave one set of group inputs blank."]
[]
[null,"With respect to virus transmission, the model assumes that individuals fall into any of three categories: susceptible, infected and removed."]
[null,"A susceptible individual is one who has not yet been infected and is thus subject to the risk of future infection."]
[null,"An infected individual (at a particular point in the projection) has an active infection, and may thus transmit the virus to others."]
[null,"A removed individual has already been infected, and the infection has run its course, resulting either in recovery or death."]
[]
[null,"The model projects the infection status of the population forward in time in one-day steps. For each step, the following calculations are performed,"]
[null,"where \"S\", \"I\" and \"R\" stand for susceptible, infected, and removed, respectively, and the subscript \"N\" represents the Nth day of the projection:"]