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How do I get my actual solution which involves _Z?

January 20, 2025, 7:51 am
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How do I get my actual solution which involves _Z? I have  tried answers that w ere given on questions related to _Z in a solution but mine is not working. I am completely new to Maple ,kindly help me.

eq1 := Lambda[h]+rho[2]*R[h]-(b[h]+kappa+beta[1])*S[h] = 0

Lambda[h]+rho[2]*R[h]-(b[h]+kappa+beta[1])*S[h] = 0

(1)

eq2 := T[h] = 0

T[h] = 0

(2)

eq3 := R[h]-kappa*S[h]/(rho[2]+b[h]) = 0

R[h]-kappa*S[h]/(rho[2]+b[h]) = 0

(3)

eq4 := Lambda[m]*L-(alpha+pi)*S[m] = 0

Lambda[m]*L-(alpha+pi)*S[m] = 0

(4)

eq5 := c(1-L/K)*S[m]-(d+Lambda[m])*L = 0

c(1-L/K)*S[m]-(d+Lambda[m])*L = 0

(5)

sol := solve({eq1, eq2, eq3, eq4, eq5}, [T[h], S[h], R[h], L, S[m]])

[[T[h] = 0, S[h] = Lambda[h]*(rho[2]+b[h])/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), R[h] = kappa*Lambda[h]/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), L = 0, S[m] = 0], [T[h] = 0, S[h] = Lambda[h]*(rho[2]+b[h])/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), R[h] = kappa*Lambda[h]/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), L = (alpha+pi)*RootOf(-c((K*Lambda[m]-_Z*alpha-_Z*pi)/(K*Lambda[m]))*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)/Lambda[m], S[m] = RootOf(-c((K*Lambda[m]-_Z*alpha-_Z*pi)/(K*Lambda[m]))*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)]]

(6)

DF := sol[1]

[T[h] = 0, S[h] = Lambda[h]*(rho[2]+b[h])/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), R[h] = kappa*Lambda[h]/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), L = 0, S[m] = 0]

(7)

DF2 := sol[2]

[T[h] = 0, S[h] = Lambda[h]*(rho[2]+b[h])/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), R[h] = kappa*Lambda[h]/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), L = (alpha+pi)*RootOf(-c((K*Lambda[m]-_Z*alpha-_Z*pi)/(K*Lambda[m]))*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)/Lambda[m], S[m] = RootOf(-c((K*Lambda[m]-_Z*alpha-_Z*pi)/(K*Lambda[m]))*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)]

(8)

"(=)"

[T[h] = 0, S[h] = Lambda[h]*(rho[2]+b[h])/(b[h]^2+(kappa+rho[2]+beta[1])*b[h]+beta[1]*rho[2]), R[h] = kappa*Lambda[h]/(b[h]^2+(kappa+rho[2]+beta[1])*b[h]+beta[1]*rho[2]), L = (alpha+pi)*RootOf(-c((K*Lambda[m]-_Z*alpha-_Z*pi)/(K*Lambda[m]))*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)/Lambda[m], S[m] = RootOf(-c((K*Lambda[m]-_Z*alpha-_Z*pi)/(K*Lambda[m]))*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)]

(9)

"(=)"

[T[h] = 0, S[h] = Lambda[h]*(rho[2]+b[h])/(b[h]^2+(kappa+rho[2]+beta[1])*b[h]+beta[1]*rho[2]), R[h] = kappa*Lambda[h]/(b[h]^2+(kappa+rho[2]+beta[1])*b[h]+beta[1]*rho[2]), L = (alpha+pi)*RootOf(-c((K*Lambda[m]-_Z*alpha-_Z*pi)/(K*Lambda[m]))*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)/Lambda[m], S[m] = RootOf(-c((K*Lambda[m]-_Z*alpha-_Z*pi)/(K*Lambda[m]))*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)]

(10)

solve({eq4, eq5}, [L, S[m]], explicit)

[[L = 0, S[m] = 0], [L = (alpha+pi)*RootOf(-c((K*Lambda[m]-_Z*alpha-_Z*pi)/(K*Lambda[m]))*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)/Lambda[m], S[m] = RootOf(-c((K*Lambda[m]-_Z*alpha-_Z*pi)/(K*Lambda[m]))*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)]]

(11)

theIndets := indets(indets(sol, atomic))

{K, L, alpha, d, kappa, pi, Lambda[h], Lambda[m], R[h], S[h], S[m], T[h], b[h], beta[1], rho[2]}

(12)

allvalues(sol)

[[T[h] = 0, S[h] = Lambda[h]*(rho[2]+b[h])/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), R[h] = kappa*Lambda[h]/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), L = 0, S[m] = 0], [T[h] = 0, S[h] = Lambda[h]*(rho[2]+b[h])/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), R[h] = kappa*Lambda[h]/(kappa*b[h]+b[h]^2+b[h]*beta[1]+b[h]*rho[2]+beta[1]*rho[2]), L = -K*(RootOf(-c(_Z)*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)-1), S[m] = -K*Lambda[m]*(RootOf(-c(_Z)*Lambda[m]+d*alpha+Lambda[m]*alpha+d*pi+Lambda[m]*pi)-1)/(alpha+pi)]]

(13)

NULL

``

Download maple_code_for_disease_equilibruim.mw

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