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Yee Voon

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How to plot phase portrait?...

Yee Voon 20 Maple
ode detools differential-equations
April 05 2018
2 0

Phase_potrait.mw
Hello, anybody knows how to plot phase potrait for disease free equilibrium?

> 

restart
> 

interface(imaginaryunit = I)

I

 (1)
> 

with(DEtools), with(linalg)
> 

k := .5; tau := .95; mu := 0.1e-1; pi := 116.1; `ϑ` := 0.8e-2; phi := 0.25e-2; `ε` := 0.2e-2; rho := 0.5e-1; beta := 0.115e-1; chi := 0.598e-2; q := .5; eta := .2; delta := .1; alpha := 0.57e-1; p := .2; Upsilon := 1.2
> 

lambda := k*tau*(C(t)*Upsilon+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t))
> 

sys := {diff(C(t), t) = rho*lambda*S(t)+rho*`ε`*lambda*V(t)+(1-q)*eta*I(t)-(mu+beta+chi)*C(t), diff(I(t), t) = (1-rho)*lambda*S(t)+(1-rho)*`ε`*lambda*V(t)+chi*C(t)-(mu+alpha+eta)*I(t), diff(R(t), t) = beta*C(t)+q*eta*I(t)-(mu+delta)*R(t), diff(S(t), t) = (1-p)*pi+phi*V(t)+delta*R(t)-(mu+lambda+`ϑ`)*S(t), diff(V(t), t) = p*pi+`ϑ`*S(t)-(lambda*`ε`+mu+phi)*V(t)}

{diff(C(t), t) = 0.2375e-1*(1.2*C(t)+I(t))*S(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.4750e-4*(1.2*C(t)+I(t))*V(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+.10*I(t)-0.2748e-1*C(t), diff(I(t), t) = .45125*(1.2*C(t)+I(t))*S(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.90250e-3*(1.2*C(t)+I(t))*V(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.598e-2*C(t)-.267*I(t), diff(R(t), t) = 0.115e-1*C(t)+.10*I(t)-.11*R(t), diff(S(t), t) = 92.88+0.25e-2*V(t)+.1*R(t)-(0.18e-1+.475*(1.2*C(t)+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t)))*S(t), diff(V(t), t) = 23.22+0.8e-2*S(t)-(0.950e-3*(1.2*C(t)+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t))+0.125e-1)*V(t)}

 (2)
> 

DEplot(sys, [S(t), V(t), C(t), I(t), R(t)], t = 0 .. 50, S = 0 .. 2, V = 0 .. 2, C = 0 .. 2, I = 0 .. 2, R = 0 .. 2, [[S(0) = 0, V(0) = 0, C(0) = 0, I(0) = 0, R(0) = 0]], stepsize = .1, linecolour = blue, thickness = 1, arrows = slim)

Error, (in DEtools/DEplot/WhichPlot) More than two dependent variables - please indicate the desired scene.

  
> 

``


 

Download Phase_potrait.mw
 

> 

restart
> 

interface(imaginaryunit = I)

I

 (1)
> 

with(DEtools), with(linalg)
> 

k := .5; tau := .95; mu := 0.1e-1; pi := 116.1; `ϑ` := 0.8e-2; phi := 0.25e-2; `ε` := 0.2e-2; rho := 0.5e-1; beta := 0.115e-1; chi := 0.598e-2; q := .5; eta := .2; delta := .1; alpha := 0.57e-1; p := .2; Upsilon := 1.2
> 

lambda := k*tau*(C(t)*Upsilon+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t))
> 

sys := {diff(C(t), t) = rho*lambda*S(t)+rho*`ε`*lambda*V(t)+(1-q)*eta*I(t)-(mu+beta+chi)*C(t), diff(I(t), t) = (1-rho)*lambda*S(t)+(1-rho)*`ε`*lambda*V(t)+chi*C(t)-(mu+alpha+eta)*I(t), diff(R(t), t) = beta*C(t)+q*eta*I(t)-(mu+delta)*R(t), diff(S(t), t) = (1-p)*pi+phi*V(t)+delta*R(t)-(mu+lambda+`ϑ`)*S(t), diff(V(t), t) = p*pi+`ϑ`*S(t)-(lambda*`ε`+mu+phi)*V(t)}

{diff(C(t), t) = 0.2375e-1*(1.2*C(t)+I(t))*S(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.4750e-4*(1.2*C(t)+I(t))*V(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+.10*I(t)-0.2748e-1*C(t), diff(I(t), t) = .45125*(1.2*C(t)+I(t))*S(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.90250e-3*(1.2*C(t)+I(t))*V(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.598e-2*C(t)-.267*I(t), diff(R(t), t) = 0.115e-1*C(t)+.10*I(t)-.11*R(t), diff(S(t), t) = 92.88+0.25e-2*V(t)+.1*R(t)-(0.18e-1+.475*(1.2*C(t)+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t)))*S(t), diff(V(t), t) = 23.22+0.8e-2*S(t)-(0.950e-3*(1.2*C(t)+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t))+0.125e-1)*V(t)}

 (2)
> 

DEplot(sys, [S(t), V(t), C(t), I(t), R(t)], t = 0 .. 50, S = 0 .. 2, V = 0 .. 2, C = 0 .. 2, I = 0 .. 2, R = 0 .. 2, [[S(0) = 0, V(0) = 0, C(0) = 0, I(0) = 0, R(0) = 0]], stepsize = .1, linecolour = blue, thickness = 1, arrows = slim)

Error, (in DEtools/DEplot/WhichPlot) More than two dependent variables - please indicate the desired scene.

  
> 

``


 

Download Phase_potrait.mw

 

 

Why I cant plot graph?...

Yee Voon 20 Maple
plot plotting
April 01 2018
1 3

Result.mw
 

Download Result.mw

Anybody know why the graph doesnt appear and what is the error in my coding?

 

 

How to solve error occur in DEtools?...

Yee Voon 20 Maple
detools differential-equations deplot3d
March 15 2018
3 0

Attractor.mw
Hello, anybody could help with this error?

> 

restart
> 

interface(imaginaryunit = j);

I

 (1)
> 

with(DEtools):
> 

k := .5; 1; tau := .95; 1; mu := 0.1e-1; 1; pi := 116.1; 1; vartheta := 0.8e-2; 1; phi := 0.25e-2; 1; epsilon := 0.2e-2; 1; rho := 0.5e-1; 1; beta := 0.115e-1; 1; chi := 0.598e-2; 1; q := .5; 1; eta := .2; 1; delta := .1; 1; alpha := 0.57e-1; 1; p := .2; 1; Upsilon := 1.2

.5

  

.95

  

0.1e-1

  

116.1

  

0.8e-2

  

0.25e-2

  

0.2e-2

  

0.5e-1

  

0.115e-1

  

0.598e-2

  

.5

  

.2

  

.1

  

0.57e-1

  

.2

  

1.2

 (2)
> 

lambda := k*tau*(C(t)*Upsilon+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t)):
> 

DEplot3d({d*C(t)/dt = rho*lambda*S(t)+rho*`ε`*lambda*V(t)+(1-q)*eta*I(t)-(mu+beta+chi)*C(t), d*I(t)/dt = (1-rho)*lambda*S(t)+(1-rho)*`ε`*lambda*V(t)+chi*C(t)-(mu+alpha+eta)*I(t), d*R(t)/dt = beta*C(t)+q*eta*I(t)-(mu+delta)*R(t), d*S(t)/dt = (1-p)*pi+phi*V(t)+delta*R(t)-(mu+lambda+`ϑ`)*S(t), d*V(t)/dt = p*pi+`ϑ`*S(t)-(lambda*`ε`+mu+phi)*V(t)}, {C(t), I(t), R(t), S(t), V(t)}, t = 0 .. 300, stepsize = .1, [[S(0) = 8200, V(0) = 2800, C(0) = 200, I(0) = 210, R(0) = 200]], linecolour = t, axes = BOXED, scene = [S, V, C, I, R])

Error, (in DEtools/DEplot/CheckInitial) the 'number' option must be specified before initial conditions

  
> 

``


 

Download Attractor.mw

 

How to simplify an equation?...

Yee Voon 20 Maple
simplify
March 11 2018
1 0

Coding_Basic_Reproduction_Number_2.mw

Anybody know how to simplify the equation?

What should I do for the error in Maple ...

Yee Voon 20 Maple
eval diff
March 05 2018
2 0

Partial_for_R0.mw
Anybody knows what happen to this coding?

> 

restart
> 

unprotect(Pi)
> 

k := .5;

.5

  

.95

  

0.1e-1

  

116.1

  

0.8e-2

  

0.25e-2

  

0.2e-2

  

0.5e-1

  

0.115e-1

  

0.598e-2

  

.5

  

.2

  

.1

  

0.57e-1

  

.2

  

1.2

 (1)
> 

R := k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(vartheta+mu+phi))+epsilon*Pi*(mu*p+vartheta)/(mu*(vartheta+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q))

65688.31239

 (2)
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), k)

Error, invalid input: diff received .5, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), `ε`)

Error, invalid input: diff received 0.2e-2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), tau)

Error, invalid input: diff received .95, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), phi)

Error, invalid input: diff received 0.25e-2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), chi)

Error, invalid input: diff received 0.598e-2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), p)

Error, invalid input: diff received .2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), `ϑ`)

Error, invalid input: diff received 0.8e-2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), mu)

Error, invalid input: diff received 0.1e-1, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), alpha)

Error, invalid input: diff received 0.57e-2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), rho)

Error, invalid input: diff received 0.5e-1, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), beta)

Error, invalid input: diff received 0.115e-1, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), eta)

Error, invalid input: diff received .2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), q)

Error, invalid input: diff received .5, which is not valid for its 2nd argument

  
> 

NULL
> 

NULL


 

Download Partial_for_R0.mw
 

> 

restart
> 

unprotect(Pi)
> 

k := .5;

.5

  

.95

  

0.1e-1

  

116.1

  

0.8e-2

  

0.25e-2

  

0.2e-2

  

0.5e-1

  

0.115e-1

  

0.598e-2

  

.5

  

.2

  

.1

  

0.57e-1

  

.2

  

1.2

 (1)
> 

R := k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(vartheta+mu+phi))+epsilon*Pi*(mu*p+vartheta)/(mu*(vartheta+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q))

65688.31239

 (2)
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), k)

Error, invalid input: diff received .5, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), `ε`)

Error, invalid input: diff received 0.2e-2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), tau)

Error, invalid input: diff received .95, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), phi)

Error, invalid input: diff received 0.25e-2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), chi)

Error, invalid input: diff received 0.598e-2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), p)

Error, invalid input: diff received .2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), `ϑ`)

Error, invalid input: diff received 0.8e-2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), mu)

Error, invalid input: diff received 0.1e-1, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), alpha)

Error, invalid input: diff received 0.57e-2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), rho)

Error, invalid input: diff received 0.5e-1, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), beta)

Error, invalid input: diff received 0.115e-1, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), eta)

Error, invalid input: diff received .2, which is not valid for its 2nd argument

  
> 

diff(k*tau*(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))*(Pi*(-mu*p+mu+phi)/(mu*(`ϑ`+mu+phi))+`ε`*Pi*(mu*p+`ϑ`)/(mu*(`ϑ`+mu+phi)))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q)), q)

Error, invalid input: diff received .5, which is not valid for its 2nd argument

  
> 

NULL
> 

NULL


 

Download Partial_for_R0.mw

 

 

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