Project 2: Elu Diacasc Epidemic Population Model years. A company has hired Dr.
ID: 3282269 • Letter: P
Question
Project 2: Elu Diacasc Epidemic Population Model years. A company has hired Dr. T's students to test and model the effects or a new flu vaccine T vaccine, the classes uses numerical techniques to solve the logistic population equation (non-linear) ss follows: a, # nP--nP2 (logistic equation) P(1)-50 (initial Let P() represent healthy test subjects who are susceptible to filu at any point in time. Let 0.0225 and r2 -0.0003 Population also affected by: Population infected with flu (F): o s,F-s,F (logistic equation) o Lots! 0.02875 and S2# 0.0009 RI-10% of PI) - Population already infected and cannot be infected again (R): A kR logistie equation o Let k 0.0052 R(1-5% ofP(1) Total Healthy Population, T(), change is the sum of changes resulting from P(t),-FO, -R (i.e. pop change - flu reinfected). Matlab programs method, b) Heun method, and c) Rungo-Kutta method for a 600 days period. Analyze the differential equation -5). What is the effect of Ax on the final answer (i.e. t-600 days) for each method? 2. numerically. Initially set At-60 days (then set As-25, and At 3. Provide graph in minutes for P(), F(, R(), and T() for each method. 4. Summanize your results for Tt) at t-600 days for each method and Ax in a table. 1) Objective of the project of met and key algorithms Results (contains tables, graphs, etc.) 3) 4) Discussion/ Analysis of your work, output and key o Due date: March 26,2018 (Men Lab) or March 28, 201s Wed Lab)Explanation / Answer
% MATLAB CODE
%Euler Method:
if nargin<4
error('at least 4 input arguments required')
end
ti= tspan(1);
tf = tspan(2);
if ~ (tf>ti)
error('upper limit must be greater than lower limit')
end
t = (ti:h:tf)';
n= length(t);
if t(n)<tf t(n+1) = tf;
n= n+1;
t(n)=tf;
end
P = P0*ones(n,1); %preallocate P to improve efficiency
F0 = 0.1*P0;
F = F0*ones(n,1);
R0 = 0.05*P0;
R = R0*ones(n,1);
for i = 1:n-1 %implementing Euler's Method
P(i+1) = P(i) + dPdt(t(i),P(i))*(t(i+1)-t(i));
F(i+1) = F(i) + dFdt(t(i),F(i))*(t(i+1)-t(i));
R(i+1) = R(i) + dRdt(t(i),R(i))*(t(i+1)-t(i));
T(i+1) = P(i+1)-F(i+1)-R(i+1);
end
plot(t,T)
dPdt=@(t,P) 0.0225*P - 0.0003*P^2 ;
dFdt=@(t,F) 0.02875F - 0.0009*F^2;
dRdt=@(t,R) 0.0052R;
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