Hi everybody,
The idea was to simulate a system of viral infections with random mutations in Mathematica, which I programmed as follows:
...
v1[0] = 1;
v2[0] = 0;
v3[0] = 0;
...
Do[o[t_] = RandomReal[]; a[t_] = RandomReal[];
v1[t_] =
v1[t - 1] + h v1[t - 1] (r (1 + ix) - p x1[t - 1] - q z[t - 1]);
w2[t_] =
v2[t - 1] + h v2[t - 1] (r (1 + ix) - p x2[t - 1] - q z[t - 1]);
w3[t_] =
v3[t - 1] + h v3[t - 1] (r (1 + ix) - p x3[t - 1] - q z[t - 1]);
x1[t_] =
x1[t - 1] +
h (c v1[t - 1] -
u x1[t - 1] (1 + v1[t - 1] + v2[t - 1] + v3[t - 1]));
x2[t_] =
x2[t - 1] +
h (c v2[t - 1] -
u x2[t - 1] (1 + v1[t - 1] + v2[t - 1] + v3[t - 1]));
x3[t_] =
x3[t - 1] +
h (c v3[t - 1] -
u x3[t - 1] (1 + v1[t - 1] + v2[t - 1] + v3[t - 1]));
z[t_] = z[t - 1] + h (( 1 - ix) k - u z[t - 1]);
v2[t_] = If[ w2[t] <= 0 && o[t] > 0.95, a[t], w2[t]];
v3[t_] =
If[ w3[t] <= 0 && o[t] > 0.95 && w2[t] > 0, a[t], w3[t]];
X1[t] = x1[t]; X2[t] = x2[t]; X3[t] = x3[t]; V1[t] = v1[t];
V2[t] = v2[t]; V3[t] = v3[t]; W2[t] = w2[t]; W3[t] = w3[t];
Z[t] = z[t]; U[t] = o[t]; A[t] = a[t], {t, 1, T}];
v[t] is the virus strain and x[t] is the anti-viral reaction (here 3 strains). However, in this case I have to programme each virus mutant a priori, set its value to zero and to a positive value whenever the condition is fulfilled. That implies that for 20 possible mutations I have to write down 20 equations both for x[t] and v[t].
Does anybody know, if there is a way to make Mathematica automatically add two equations to the do function whenever the condition is met?
Thanks!