PROBLEM 24 - 0591: regions, A and B, is The population flow between two assumed to be proportional to the difference in population density between the areas. Let N1 (t), N2(t) be the populations in...

Extracted text: PROBLEM 24 - 0591: regions, A and B, is The population flow between two assumed to be proportional to the difference in population density between the areas. Let N1 (t), N2(t) be the populations in regions A and B respectively, with N1 (0) = N1o and %3D N2(0) = N20 - The natural (i.e., in absence of immigration) rates of growth of the regions (per unit of time) are given by the following formulas : Case (1): (1) rN1 N2 = (b - mN2/2N20)N2 (2) Case (2): (3) Nj = k(S - N1) N2 = (4) N1 = k(S - 12N2 Case (3): N7) (5) N2 = (b - (6) where r,r2,b,m,k are positive mN2/2N20)N2 constants, 0 < k="">< 1.="" write="" a="" fortran="" program="" which="" uses="" the="" modified="" euler="" method="" to="" simulate="" this="" system="" from="" t="0" to="" t="tf">