Question

Part A - SIR model for the spread of disease Overview. This part of the assignment uses a mix of theory and data to estimate the contact number c=b/k of an epidemic and hence to estimate the infection-spreading parameter b. The point is that once you know the value of b for a certain disease and population, you can use it in your model the next time there is an cpidemic, thus cnabling you to make predictions about the demand for doctors and hospital facilities. Note: In the current covid-19 pandemic, this ratio is similar to the basic reproduction number Ro. Source Material (click to download): The Contact Number https://www.maa.org/press/periodicals/loci/jos/the-air-model-for-aprend-of-dienne-the-contact-number Read the Instructions below. Then do Problems 1-5 in "The Contact Number". In(1/800) СЕ 1-800 so that both the numerator and denominator are positive. • In Problem 5, to evaluate soc graphically, use your numerical solution from Homework 4 (Relating Model Parameters to Data), with k=1/3 and b= 1 and initial conditions (0) = 1 and i(0) = 1.27 x 10-6 Copy or print the graphs for s(t) and i(t), and include them with this homework. Indicate on your graph the value of sco Then show how this value leads to an estimated value of the contact number c. accurate graphical estimate of So. You may use the online plotter: (https://homepages. bluffton.edu/-nesterd/java/slopefields.html) Recall that we study the DEs for s(t) and i(t) and omit the equation for the recovered fraction r(t) (which could then be found from r(t) =1-8(t) -(0)

Answer 1

= -bst) ict at bsct ect) - kict) d = i de cusing chain rule bsi-ki= di (absi) dele - 1 + B - (di= fas + fes as (icts = us + Insta) Now : i = -stenstq = its , lns = constant I hence its- ens is independent ay time. .. ico) + scoo- I ln sco) = is too - I lnso 1 - 1 = 0 + Soo (Insa la 20 C=ensoo (2001) I SCO) 21 (coozo

susceptible infected Population Density - 20 40 60 - 80 - 100 Time

(5) Graph for Numerical time plot has been plotted. It can be seen that after suldicient time so z 0,06 I encllo.06) 05 2101 0,94 C = -0.06 - 2.99 Also both c= are 1/R = 3 equal,
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