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ashy 8

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These are questions asked by ashy

substitute equation to equation...

ashy 35 Maple 18
substitution incomplete-question
June 17 2025
1 3

I want to substitute equation to equation, how?

Download r.mw

how to give a limit value from -1 to 1 f...

ashy 35 Maple 18
sensitivity
March 29 2025
2 10

I will look for sensitivity analysis for parameters in the epidemic model using the normalization formula, the result should be between -1 to 1 but there are 2 parameters whose values ​​are more than 1, how do I set the limit so that the sensitivity value is between -1 to 1?

> 

restart
> 

with(VectorCalculus):
> 

with(linalg):
> 

_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)
> 

Ro := VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(Lambda, alpha), beta), r), xi), VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(K, eta), phi)), VectorCalculus:-`*`(VectorCalculus:-`*`(K, eta), r)), 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)
> 

`as1_Λ` := VectorCalculus:-`*`(diff(Ro, Lambda), VectorCalculus:-`*`(Lambda, 1/Ro));

1

 (3)
> 

`as1_μ` := VectorCalculus:-`*`(diff(Ro, mu), VectorCalculus:-`*`(mu, 1/Ro));

(-Lambda*alpha*beta*r*xi*(-K*eta*phi+K*eta*r-r)/(mu^2*(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))-Lambda*alpha*beta*r^2*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)^2*(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))*mu^2*(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)/(Lambda*alpha*beta*r*xi*(-K*eta*phi+K*eta*r-r))

 (4)
> 

`as1_η` := VectorCalculus:-`*`(diff(Ro, eta), VectorCalculus:-`*`(eta, 1/Ro));

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

 (5)
> 

`as1_β` := VectorCalculus:-`*`(diff(Ro, beta), VectorCalculus:-`*`(beta, 1/Ro));

(Lambda*alpha*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))-Lambda*alpha*beta*r*xi*(-K*eta*phi+K*eta*r-r)*(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)^2*(delta+gamma+mu)))*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)/(Lambda*alpha*r*xi*(-K*eta*phi+K*eta*r-r))

 (6)
> 

`as1_θ` := VectorCalculus:-`*`(diff(Ro, theta), VectorCalculus:-`*`(theta, 1/Ro));

-r*theta/(K*beta*eta*phi-K*beta*eta*r+beta*r+mu*r+r*theta)

 (7)
> 

`as1_τ` := VectorCalculus:-`*`(diff(Ro, tau), VectorCalculus:-`*`(tau, 1/Ro));

r*tau/(K*phi*sigma-K*r*sigma-r*tau)

 (8)
> 

as1_r := VectorCalculus:-`*`(diff(Ro, r), VectorCalculus:-`*`(r, 1/Ro));

(Lambda*alpha*beta*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))+Lambda*alpha*beta*r*xi*(K*eta-1)/(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))-Lambda*alpha*beta*r*xi*(-K*eta*phi+K*eta*r-r)*(-K*sigma-tau)/(mu*(K*phi*sigma-K*r*sigma-r*tau)^2*(K*beta*eta*phi-K*beta*eta*r+beta*r+mu*r+r*theta)*(delta+gamma+mu))-Lambda*alpha*beta*r*xi*(-K*eta*phi+K*eta*r-r)*(-K*beta*eta+beta+mu+theta)/(mu*(K*phi*sigma-K*r*sigma-r*tau)*(K*beta*eta*phi-K*beta*eta*r+beta*r+mu*r+r*theta)^2*(delta+gamma+mu)))*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)/(Lambda*alpha*beta*xi*(-K*eta*phi+K*eta*r-r))

 (9)
> 

`as1_φ` := VectorCalculus:-`*`(diff(Ro, phi), VectorCalculus:-`*`(phi, 1/Ro));

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

 (10)
> 

param := Lambda = 0.133e-1, alpha = 0.7954551e-1, delta = .9, K = 300, r = 0.76e-1, tau = 0.900982e-1, gamma = 0.917e-2, mu = 0.56e-3, phi = 0.9e-1, eta = 0.9e-2, sigma = 0.456e-3, beta = .567, theta = 0.9e-2, xi = 0.487e-1:
> 

subs(param, `svΛ` = `as1_Λ`);

`svΛ` = 1

  

`svμ` = -1.001267817

  

`svη` = 0.3698561176e-2

  

`svβ` = 0.1113482136e-1

  

`svθ` = -0.1048257226e-1

  

`svτ` = -1.388300446

  

svr = -2.519993617

  

`svφ` = 2.519993621

 (11)
 

``

Download sensitivity.mw

How to substitute a part of equation wit...

ashy 35 Maple 18
substitution simplification duplicate-question
March 11 2025
1 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

does remove_RootOf command affect the re...

ashy 35 Maple 18
rootof incomplete-question
February 25 2025
1 0

I have an epidemic model and the endemik equilibrium point contains rootOf _Z, here's one of the example

i still don't understand about the _Z and find the "remove_RootOf" command. Does it affect the result or is it an explicit result of Z?

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