We have three equations dS/dt = - a*S*| dl/dt = a*S*| - r*| dR/dt = r*| Notice what is subtracted from S is added to I, and what is added to R is subtraced from R. The table to the right summarizes how the disease spreads. The numbers will now represent percentages of a population (This helps avoid rounding errors that accumulate). 0.50 0.10 Day New Infections ( New Recoveries Susceptible Infected Recovered Susceptible, Infected, and Recovered 99.00% 1.00% 0.00% - Susceptible - Infected - Recovered 0.50% 0. 10% 98.51% 1.40% 0. 10% 0.14% 1.94% 0.24% 100.00% 0.69% 97.82% 0.95% 0. 19% 96.87% 2.70% 0.43% 1.31% 0.27% 95.56% 3.74% 0.70% 75.00% 1.78% 0.37% 93.78% 5.15% 1.08% 2.41% 0.51% 91.36% 7.05% 1.59% 3.22% 0.70% 88.14% 9.56% 2.30% 50.00% 4.21% 0.96% 83.93% 12.82% 3.25% 5.38% 1.28% 78.55% 16.91% 4.53% 25.00% 10 6.64% 1.69% 71.91% 21.86% 6.23% 11 7.86% 2.19% 64.05% 27.54% 8.41% 12 8.82% 2.75% 55.23% 33.61% 11.17% 0.00% 13 9.28% 3.36% 45.95% 39.52% 14.53% 0 10 20 30 14 9.08% 3.95% 36.87% 44.65% 18.48% Day 15 8.23% 4.47% 28.64% 48.42% 22.94% 16 6.93% 4.84% 21.70% 50.51% 27.79% 17 5.48% 5.05% 16.22% 50.94% 32.84% 18 4.13% 5.09% 12.09% 49.98% 37.93% 19 3.02% 5.00% 9.07% 48.00% 42.93% 20 2.18% 4.80% 6.89% 45.38% 47.73%21 1.56% 4.54% 5.33% 42.40% 52.27% 22 1.13% 4.24% 4.20% 39.29% 56.51% 23 0.82% 3.93% 3.37% 36.19% 60.44% 24 0.61% 3.62% 2.76% 33.18% 64.06% 25 0.46% 3.32% 2.31% 30.32% 67.37% 26 0.35% 3.03% 1.96% 27.64% 70.41% 27 0.27% 2.76% 1.69% 25.15% 73.17% 28 0.21% 2.51% 1.47% 22.84% 75.68% 29 0.17% 2.28% 1.31% 20.73% 77.97% 30 0.14% 2.07% 1.17% 18.79% 80.04% Play around with different pairs of a and r values. Try the following pairs, and describe how the disease spreads through the community (What percentage never get sick? Whats the largest percent of people sick at the same time?) a=0.9, 1=0.2 a=0.9, 1=0.5 a=0.7, 1=0.4