The main concept is to adjust model parameters so that the model-computed infections matches the infections estimated from test data. The top graph (screenshot below) provides visual feedback for evaluating the closeness of the match. The red line in this graph is model-computed infections while the black line is the infections estimated from test data. Parameters for the test-data-based estimation are found in the cells with black borders (C2, C3, C4, and C5) while the parameters for the model are in cells with red borders (C8 through C18, A26 through A45, and C26 through C45). The greyed-out cells are automatically calculated and should not be altered.
Setting the infection estimation parameters is the first thing to get done. Use cell C2 to load data from a state you want to see, using the state’s abbreviation. “US” is an option to load data for the whole country, and DC is available for the capital along with a few other abbreviations for various territories. But the data for the territories tend to have serious problems. The yellow and purple lines (testing and positive results) in the second chart are determined by the abbreviation entered in cell C2. Cell C3 is a very important parameter. It sets the ratio of actual infections up until the first maximum in cases last April to infections that were published as positive test results. So a value of 5 tunes the estimation so that at the time of the peak, the number of accumulated estimated infections is five times more than the accumulated number of published positive test results. That ratio goes down as time goes on and testing increases. Cell C4 determines a backwards time-shift applied to the estimated infections due to the delay from the date of infection to the date of a positive test result. A value of -1 in this cell turns on a dynamic delay that ranges between 9 and 15 days, depending on the availability of testing and the positivity rate. A value of 0 or greater sets a static delay at that value – in days. Cell C5 is an automated cell displaying the population of the selected state in millions. Estimated infections, (the black line on the first two charts) depends on cells C2, C3, and C4.
Setting the model parameters: cells C8 and C9 set the starting time and number of initially contagious people at that time. The model results are particularly sensitive to the initial count of contagious people and should be the first parameter to be set once a state or national numbers are chosen. Cells C11 and C12 set the time period during which a person is contagious relative to the date of infection. These have a default of 5 and 10, based on a fit to data from Washington DC. Chance of re-infection in cell C13 sets the fractional probability someone is counted as susceptible instead of immune when he recovers (reaches the end of the contagious period). The time range for loss of immunity -relative to the end date of the contagious period – is set in cells C14 and C15. Cell C16 sets the delay between vaccination and the resulting immunity while cells C17 and C18 set the time range for the duration of immunity. C19 sets the fractional rate of success of administered vaccines. C20 sets the fraction of people who have natural immunity that deliberately avoid the vaccine. Cell C21 sets the fraction of the population that is immune due to exposure to similar infections. C22 sets the fractional probability that a contagious person dies -at the end of the contagious period. Cell C23 sets a reference level that appears as a dashed line in the third graph. This level serves two purposes: one is to provide a line of comparison as the model parameters are adjusted and the vertical scale shifts around to accommodate the model results, the other purpose is to mark a level where hospital capacity is exceeded. Note that the number for the reference level is set in contagious people per 100,000 population.
The Transmission Rate Table (cells A31 to A50 and C31 to C50) is where most of the work of fitting the model to the test data is done. The table is set up for you to enter times in column A as a number of days after the start date set in cell C8. Column B displays the date for the day chosen in column A. Column C is where you set the transmission rate (R0) beginning at the time specified the same row of column A.
The Vaccination Rate Table sets the rate of vaccination delivery.
The third graph gives a look into the model, showing the number of contagious people per 100,000 of the population (orange line – not to be confused with model infections), a plot of the transmission rates (blue line), the number of of immune people per 1000 of the population (green line), the reference level (black dashed line), and a vertical yellow line to mark the date at which testing data ends. This graph also facilitates visual feedback on what the model forecasts, based on what you enter in the Transmission Rate Table.
The fourth graph shows the total percent of the population that is immune with a breakdown between natural immunity (background and recovered from infection) and vaccine-based immunity.