Advanced Search

Question: How to substitute a part of equation with another equation?

Question:How to substitute a part of equation with another equation?

ashy 35 Maple 18
substitution simplification duplicate-question
March 11 2025
2

i have an equilibrium, i want to simplify SEkuil_End[1] but with R0 eq in the simplify, how can i do that?

> 

restart
> 

with(VectorCalculus):
> 

with(linalg):
> 

with(DETools):
> 

with(DynamicSystems):
> 

_local(I):

I

  

Warning, The imaginary unit, I, has been renamed _I

  
> 

dS := VectorCalculus:-`+`(VectorCalculus:-`+`(Lambda, VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(alpha, S), P))), VectorCalculus:-`-`(VectorCalculus:-`*`(mu, S)));

-P*S*alpha-S*mu+Lambda

  

alpha*S*P-(-T*eta+1)*beta*E-theta*E-mu*E

  

(-T*eta+1)*beta*E-delta*I-gamma*I-mu*I

  

E*theta+I*gamma-R*mu

  

-P*T*sigma+I*xi-P*tau

  

r*T*(1-T/K)-phi*T

 (1)
> 

SEkuil := solve({dE, dI, dP, dR, dS, dT}, {E, I, P, R, S, T}):
> 

SEkuil_End := SEkuil[4]:
> 

R0 := VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(Lambda, alpha), beta), r), xi), VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, eta), r), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, eta), phi))), VectorCalculus:-`-`(r))), 1/VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(mu, VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, phi), sigma), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, r), sigma))), VectorCalculus:-`-`(VectorCalculus:-`*`(r, tau)))), VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, beta), eta), phi), VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, beta), eta), r))), VectorCalculus:-`*`(beta, r)), VectorCalculus:-`*`(mu, r)), VectorCalculus:-`*`(r, theta))), VectorCalculus:-`+`(VectorCalculus:-`+`(delta, gamma), mu)));

Lambda*alpha*beta*r*xi*(-K*eta*phi+K*eta*r-r)/(mu*(K*phi*sigma-K*r*sigma-r*tau)*(K*beta*eta*phi-K*beta*eta*r+beta*r+mu*r+r*theta)*(delta+gamma+mu))

 (2)
> 

SEkuil_End[1]

E = (K^2*beta*delta*eta*mu*phi^2*sigma-2*K^2*beta*delta*eta*mu*phi*r*sigma+K^2*beta*delta*eta*mu*r^2*sigma+K^2*beta*eta*gamma*mu*phi^2*sigma-2*K^2*beta*eta*gamma*mu*phi*r*sigma+K^2*beta*eta*gamma*mu*r^2*sigma+K^2*beta*eta*mu^2*phi^2*sigma-2*K^2*beta*eta*mu^2*phi*r*sigma+K^2*beta*eta*mu^2*r^2*sigma+K*Lambda*alpha*beta*eta*phi*r*xi-K*Lambda*alpha*beta*eta*r^2*xi-K*beta*delta*eta*mu*phi*r*tau+K*beta*delta*eta*mu*r^2*tau-K*beta*eta*gamma*mu*phi*r*tau+K*beta*eta*gamma*mu*r^2*tau-K*beta*eta*mu^2*phi*r*tau+K*beta*eta*mu^2*r^2*tau+K*beta*delta*mu*phi*r*sigma-K*beta*delta*mu*r^2*sigma+K*beta*gamma*mu*phi*r*sigma-K*beta*gamma*mu*r^2*sigma+K*beta*mu^2*phi*r*sigma-K*beta*mu^2*r^2*sigma+K*delta*mu^2*phi*r*sigma-K*delta*mu^2*r^2*sigma+K*delta*mu*phi*r*sigma*theta-K*delta*mu*r^2*sigma*theta+K*gamma*mu^2*phi*r*sigma-K*gamma*mu^2*r^2*sigma+K*gamma*mu*phi*r*sigma*theta-K*gamma*mu*r^2*sigma*theta+K*mu^3*phi*r*sigma-K*mu^3*r^2*sigma+K*mu^2*phi*r*sigma*theta-K*mu^2*r^2*sigma*theta+Lambda*alpha*beta*r^2*xi-beta*delta*mu*r^2*tau-beta*gamma*mu*r^2*tau-beta*mu^2*r^2*tau-delta*mu^2*r^2*tau-delta*mu*r^2*tau*theta-gamma*mu^2*r^2*tau-gamma*mu*r^2*tau*theta-mu^3*r^2*tau-mu^2*r^2*tau*theta)/((K*eta*phi-K*eta*r+r)*xi*beta*(K*beta*eta*phi-K*beta*eta*r+beta*r+mu*r+r*theta)*alpha)

 (3)
 

``

Download end.mw
Please Wait...