34. The spread of a disease through a population of 100 individ- uals is represented by the following SIRS model: ds dt

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34 The Spread Of A Disease Through A Population Of 100 Individ Uals Is Represented By The Following Sirs Model Ds Dt 1 (392.88 KiB) Viewed 23 times

34. The spread of a disease through a population of 100 individ- uals is represented by the following SIRS model: ds dt 1 R 10 1 -SI 100 1 dl dt = 1 SI 100 1 dR dt 1 -R 10 2 In this problem we will sketch the directions of the solution in the SI-plane. (a) Eliminate R to rewrite the equation system as a system of differential equations in the dependent variables S and I. (b) Draw the zero isoclines of your system from part (a). (e) Find all of the equilibria for this model and classify them (e.g., as stable nodes, unstable nodes, or saddles) by analyzing the lin- earized system. (d) Add to your plot from part (b) arrows showing the direction of the vector field on the isoclines, and in the regions between the isoclines. 0