% Example 4.4 of H.J. Oberle and H.J. Pesch, Numerical treatment of % delay differential equations by Hermite interpolation, Numer. Math., % 37 (1981) 235-255. This is a model for the spread of an infection % due to Hoppensteadt and Waltman. It is interesting because there are % discontinuous changes in the equation at known times. Oberle and Pesch % solve the problem for several values of the parameter r, namely 0.2, % 0.3, 0.4, 0.5. The example is also interesting in that values of the % derivative of the solution are required for another function of interest. r = 0.5; c = 1/sqrt(2); opts = ddeset('Jumps',[(1-c), 1, (2-c)],... 'RelTol',1e-5,'AbsTol',1e-8); sol = dde23('exam5f',1,10,[0, 10],opts,r); y10 = ddeval(sol,10); fprintf('DDE23 computed y(10) =%15.11f.\n',y10); fprintf('Reference solution y(10) =%15.11f.\n',0.06302089869); plot(sol.x,sol.y) title(['Figure 5a. Hoppensteadt-Waltman model with r = ',... num2str(r),'.']) xlabel('time t') ylabel('y(t)') Ioft = -(1/r)*(sol.yp ./ sol.y); figure plot(sol.x,Ioft) title(['Figure 5b. Hoppensteadt-Waltman model with r = ',... num2str(r),'.']) xlabel('time t') ylabel('I(t)')