Elisha

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8 years, 111 days

MaplePrimes Activity


These are questions asked by Elisha

Someone should please help me compute the left and right eigenvectors of the system below. The purpose is to compute values for 'a' and 'b' in the bifurcation formula.

Thank you

``

with(VectorCalculus)

 

(1)

interface(imaginaryunit = I)

I

(2)

I

I

(3)
 

diff(S(t), t) := `Λ__p`-(`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("θ",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`/N[p]+µ__C)*S+`ω__B`*I__B

Lambda__p-(`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("θ",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`/N[p]+µ__C)*S+omega__B*I__B

(4)

diff(I__B(t), t) := `#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("θ",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`*S/N[p]-`ω__B`*I__B-(`σ__B`+µ__C)*I__B

`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("θ",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`*S/N[p]-omega__B*I__B-(sigma__B+µ__C)*I__B

(5)

NULL

``

(6)

diff(S__A(t), t) := `Λ__A`-(µ__A+`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("α",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`/N[p])*S__A+`δ__A`*I__A

Lambda__A-(µ__A+`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("α",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`/N[p])*S__A+delta__A*I__A

(7)

diff(I__A(t), t) := `#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("α",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`*S__A/N[p]-(µ__A+`δ__A`)*I__A

`#mrow(mi("ϕ",fontstyle = "normal"),mo("⋅"),msub(mi("α",fontstyle = "normal"),mi("B")),mo("⋅"),msub(mi("I"),mi("B")))`*S__A/N[p]-(µ__A+delta__A)*I__A

(8)

NULL

``

(9)

Download CBD2.mw

Someone please help me with the computation of the right and left eigenvectors. my system of equation is attached below

with(VectorCalculus):

 

interface(imaginaryunit = I)

I

(2)

I

I

(3)

sqrt(-4)

2*I

(4)

NULL

``

Limit(N(t) = N__0*exp(-mu*t)+exp(mu*t)*K/mu, t = infinity)

 

limit(N(t), t = infinity) = limit(N__0*exp(-mu*t)+exp(mu*t)*K/mu, t = infinity)

(5)

 

NULL

#to calculate the  disease free equilibrium,

NULL

E1 := -S*µ__C+`Λ__p`

-S*µ__C+Lambda__p

(6)

NULL

``

(7)

E3 := -S__A*µ__A+`Λ__A`

-S__A*µ__A+Lambda__A

(8)

NULL

``

(9)

NULL

``

(10)

NULL

solve({E1 = 0, E3 = 0}, {S, S__A})

{S = Lambda__p/µ__C, S__A = Lambda__A/µ__A}

(11)

NULL

NULL#to calculate the Endemic Equilibrium state,

Typesetting:-mparsed()

(12)

restart

with(VectorCalculus):

 

interface(imaginaryunit = I)

I

(14)

I

I

(15)

sqrt(-4)

2*I

(16)

``

E1 := `Λ__p`-(`ϕ`*`θ__B`*I__A/N__p+µ__C)*S+`ω__B`*I__B

Lambda__p-(varphi*theta__B*I__A/N__p+µ__C)*S+omega__B*I__B

(17)

E2 := `ϕ`*`θ__B`*I__A*S/N__p-`ω__B`*I__B-(`σ__B`+µ__C)*I__B

varphi*theta__B*I__A*S/N__p-omega__B*I__B-(sigma__B+µ__C)*I__B

(18)

``

(19)

E3 := `Λ__A`-(µ__A+`ϕ`*`α__B`*I__B/N__p)*S__A+`δ__A`*I__A

Lambda__A-(µ__A+varphi*alpha__B*I__B/N__p)*S__A+delta__A*I__A

(20)

E4 := `ϕ`*`α__B`*I__B*S__A/N__p-(µ__A+`δ__A`)*I__A

varphi*alpha__B*I__B*S__A/N__p-(µ__A+delta__A)*I__A

(21)

NULL

``

(22)

NULL

``

(23)

solve({E1 = 0, E2 = 0, E3 = 0, E4 = 0}, {I__A, I__B, S, S__A})

{I__A = 0, I__B = 0, S = Lambda__p/µ__C, S__A = Lambda__A/µ__A}, {I__A = -(N__p^2*µ__A^2*µ__C^2+N__p^2*µ__A^2*µ__C*omega__B+N__p^2*µ__A^2*µ__C*sigma__B+N__p^2*µ__A*µ__C^2*delta__A+N__p^2*µ__A*µ__C*delta__A*omega__B+N__p^2*µ__A*µ__C*delta__A*sigma__B-varphi^2*Lambda__A*Lambda__p*alpha__B*theta__B)/(varphi*µ__A*theta__B*(N__p*µ__A*µ__C+N__p*µ__A*sigma__B+N__p*µ__C*delta__A+N__p*delta__A*sigma__B+varphi*Lambda__p*alpha__B)), I__B = -(N__p^2*µ__A^2*µ__C^2+N__p^2*µ__A^2*µ__C*omega__B+N__p^2*µ__A^2*µ__C*sigma__B+N__p^2*µ__A*µ__C^2*delta__A+N__p^2*µ__A*µ__C*delta__A*omega__B+N__p^2*µ__A*µ__C*delta__A*sigma__B-varphi^2*Lambda__A*Lambda__p*alpha__B*theta__B)/(alpha__B*(N__p*µ__A*µ__C^2+N__p*µ__A*µ__C*omega__B+N__p*µ__A*µ__C*sigma__B+varphi*µ__C*Lambda__A*theta__B+varphi*Lambda__A*sigma__B*theta__B)*varphi), S = (N__p*µ__A*µ__C+N__p*µ__A*sigma__B+N__p*µ__C*delta__A+N__p*delta__A*sigma__B+varphi*Lambda__p*alpha__B)*µ__A*N__p*(µ__C+omega__B+sigma__B)/(alpha__B*varphi*(N__p*µ__A*µ__C^2+N__p*µ__A*µ__C*omega__B+N__p*µ__A*µ__C*sigma__B+varphi*µ__C*Lambda__A*theta__B+varphi*Lambda__A*sigma__B*theta__B)), S__A = N__p*(N__p*µ__A^2*µ__C^2+N__p*µ__A^2*µ__C*omega__B+N__p*µ__A^2*µ__C*sigma__B+N__p*µ__A*µ__C^2*delta__A+N__p*µ__A*µ__C*delta__A*omega__B+N__p*µ__A*µ__C*delta__A*sigma__B+varphi*µ__A*µ__C*Lambda__A*theta__B+varphi*µ__A*Lambda__A*sigma__B*theta__B+varphi*µ__C*Lambda__A*delta__A*theta__B+varphi*Lambda__A*delta__A*sigma__B*theta__B)/(varphi*µ__A*theta__B*(N__p*µ__A*µ__C+N__p*µ__A*sigma__B+N__p*µ__C*delta__A+N__p*delta__A*sigma__B+varphi*Lambda__p*alpha__B))}

(24)

``

J := Jacobian([E1, E2, E3, E4], [S, I__B, S__A, I__A])

Matrix(%id = 18446746854857131062)

(25)

NULL

restart

J := Matrix(4, 4, {(1, 1) = -`ϕ`*`θ__B`*I__A/N__p-µ__C, (1, 2) = `ω__B`, (1, 3) = 0, (1, 4) = -`ϕ`*`θ__B`*S/N__p, (2, 1) = `ϕ`*`θ__B`*I__A/N__p, (2, 2) = -`ω__B`-`σ__B`-µ__C, (2, 3) = 0, (2, 4) = `ϕ`*`θ__B`*S/N__p, (3, 1) = 0, (3, 2) = -`ϕ`*`α__B`*S__A/N__p, (3, 3) = -µ__A-`ϕ`*`α__B`*I__B/N__p, (3, 4) = `δ__A`, (4, 1) = 0, (4, 2) = `ϕ`*`α__B`*S__A/N__p, (4, 3) = `ϕ`*`α__B`*I__B/N__p, (4, 4) = -µ__A-`δ__A`})

Matrix(%id = 18446746579340105118)

(26)

S := `Λ__p`/µ__C

Lambda__p/µ__C

(27)

S__A := `Λ__A`/µ__A

Lambda__A/µ__A

(28)

I__B := 0

0

(29)

I__A := 0

0

(30)

NULL

0

(31)

J := Matrix(4, 4, {(1, 1) = -`ϕ`*`θ__B`*I__A/N__p-µ__C, (1, 2) = `ω__B`, (1, 3) = 0, (1, 4) = -`ϕ`*`θ__B`*S/N__p, (2, 1) = `ϕ`*`θ__B`*I__A/N__p, (2, 2) = -`ω__B`-`σ__B`-µ__C, (2, 3) = 0, (2, 4) = `ϕ`*`θ__B`*S/N__p, (3, 1) = 0, (3, 2) = -`ϕ`*`α__B`*S__A/N__p, (3, 3) = -µ__A-`ϕ`*`α__B`*I__B/N__p, (3, 4) = `δ__A`, (4, 1) = 0, (4, 2) = `ϕ`*`α__B`*S__A/N__p, (4, 3) = `ϕ`*`α__B`*I__B/N__p, (4, 4) = -µ__A-`δ__A`})

Matrix(%id = 18446746579340107518)

(32)

J := Matrix(4, 4, {(1, 1) = -µ__C, (1, 2) = `ω__B`, (1, 3) = 0, (1, 4) = -`β__1`, (2, 1) = 0, (2, 2) = -`ω__B`-`σ__B`-µ__C, (2, 3) = 0, (2, 4) = -`β__1`, (3, 1) = 0, (3, 2) = -`β__2`, (3, 3) = -µ__A, (3, 4) = `δ__A`, (4, 1) = 0, (4, 2) = `β__2`, (4, 3) = 0, (4, 4) = -µ__A-`δ__A`})

Matrix(%id = 18446746579417403630)

(33)

"simplify( ? )"

Matrix(%id = 18446746579305905318)

(34)

"LinearAlgebra:-Eigenvalues( ? )"

Vector[column](%id = 18446746579445964182)

(35)

"LinearAlgebra:-CharacteristicPolynomial( ?, lambda )"

lambda^4+(2*µ__A+delta__A+omega__B+sigma__B+2*µ__C)*lambda^3+(beta__1*beta__2+µ__A^2+4*µ__A*µ__C+µ__A*delta__A+2*µ__A*omega__B+2*µ__A*sigma__B+µ__C^2+2*µ__C*delta__A+µ__C*omega__B+µ__C*sigma__B+delta__A*omega__B+delta__A*sigma__B)*lambda^2+(beta__1*beta__2*µ__A+beta__1*beta__2*µ__C+2*µ__A^2*µ__C+µ__A^2*omega__B+µ__A^2*sigma__B+2*µ__A*µ__C^2+2*µ__A*µ__C*delta__A+2*µ__A*µ__C*omega__B+2*µ__A*µ__C*sigma__B+µ__A*delta__A*omega__B+µ__A*delta__A*sigma__B+µ__C^2*delta__A+µ__C*delta__A*omega__B+µ__C*delta__A*sigma__B)*lambda+beta__1*beta__2*µ__A*µ__C+µ__A^2*µ__C^2+µ__A^2*µ__C*omega__B+µ__A^2*µ__C*sigma__B+µ__A*µ__C^2*delta__A+µ__A*µ__C*delta__A*omega__B+µ__A*µ__C*delta__A*sigma__B

(36)

NULL

"(->)"

Vector[column](%id = 18446746579340117046)

(37)

# to find the trace we

 

Matrix(7, 7, {(1, 1) = -beta*lambda-v__1-µ, (1, 2) = v__2, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (2, 1) = v__1, (2, 2) = beta*(w-1)*lambda-µ-v__2-alpha, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (3, 1) = 0, (3, 2) = alpha, (3, 3) = -µ, (3, 4) = 0, (3, 5) = `ρ__A`, (3, 6) = `ρ__F`, (3, 7) = -(-1+k)*`ρ__Q`, (4, 1) = beta*lambda, (4, 2) = -beta*(w-1)*lambda, (4, 3) = 0, (4, 4) = -q__E-delta-µ, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = a*delta, (5, 5) = -`ρ__A`-q__A-µ, (5, 6) = 0, (5, 7) = k*`ρ__Q`, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = -delta*(-1+a), (6, 5) = 0, (6, 6) = -`ρ__F`-q__F-`δ__F`-µ, (6, 7) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = q__E, (7, 5) = q__A, (7, 6) = q__F, (7, 7) = -`ρ__Q`-`δ__Q`-µ})

Matrix(%id = 36893490965935089652)

(38)

"(->)"

-beta*lambda-v__1-7*µ+beta*(w-1)*lambda-v__2-alpha-q__E-delta-rho__A-q__A-rho__F-q__F-delta__F-rho__Q-delta__Q

(39)

 

#this shows that trace is negative

 

#to Achieve stability, the value below must be less than zero

 

(-q__E-delta-µ)*(-`&rho;__F`-q__F-`&delta;__F`-µ)*(-k*q__A*`&rho;__Q`+q__A*µ+q__A*`&delta;__Q`+q__A*`&rho;__Q`+µ^2+µ*`&delta;__Q`+µ*`&rho;__A`+µ*`&rho;__Q`+`&delta;__Q`*`&rho;__A`+`&rho;__A`*`&rho;__Q`)*µ < 0

(-q__E-delta-µ)*(-rho__F-q__F-delta__F-µ)*(-k*q__A*rho__Q+q__A*rho__Q+q__A*µ+q__A*delta__Q+rho__A*rho__Q+rho__A*µ+rho__A*delta__Q+rho__Q*µ+µ^2+µ*delta__Q)*µ < 0

(40)

 NULL

M := diff(N(t), t) = Pi-µ*N(t)

diff(N(t), t) = Pi-µ*N(t)

(41)

dsolve({M}, N(t))

{N(t) = Pi/µ+exp(-µ*t)*_C1}

(42)

eval({N(t) = Pi/µ+exp(-µ*t)*_C1}, [t = infinity])

{N(infinity) = Pi/µ+exp(-µ*infinity)*_C1}

(43)

value(%)

{N(infinity) = Pi/µ+exp(-µ*infinity)*_C1}

(44)

Limit(N(t) = Pi/µ+exp(-µ*t)*_C1, t = infinity); value(%)

Limit(N(t) = Pi/µ+exp(-µ*t)*_C1, t = infinity)

 

limit(N(t), t = infinity) = limit(Pi/µ+exp(-µ*t)*_C1, t = infinity)

(45)

 

Subs := diff(S(t), t) = -(beta*lambda+v__1+µ)*S(t)

diff(S(t), t) = -(beta*lambda+v__1+µ)*S(t)

(46)

dsolve({Subs}, S(t))

{S(t) = _C1*exp(-(beta*lambda+v__1+µ)*t)}

(47)
 

``

Download Cotton_DFE_and_Jacobian.mw

Please, I am encountering error trying to run these codes for sensitivity analysis using the formula for sensitivity analysis

``

restart;

#
# Set up numerical values for all problem parameters
#
  params:=[ Lambda__p=100,         gamma__B=0.05,      gamma__B=0.05,
                 gamma__C=0.01, omega__C=0.001,  omega__B=0.001,
            sigma__B=0.0001,     sigma__C=0.01, sigma__BC=0.01,
                theta__B=0.8,     theta__C=0.5,      mu__C=1.0,
              Lambda__A=1.0,       Lambda__w=1.0,   varphi__8.33,
            mu__A=1.0, mu__w=1.0, alpha__B=0.005, alpha__C=0.005, alpha__BC=0.15, Zeta__B=0.5, Zeta__C=0.5, delta__A=0.66, delta__w=1.33
          ]:

#
# Define main function
#
  R:= (varphi^2*theta__B*Lambda__p*alpha__B*Lambda__A)/((mu__c*mu__A*N__p^2)*(mu__A*mu__c+mu__A*omega__B+mu__A*sigma__B+mu__c*delta__A+delta__A*omega__B+delta__A*sigma__B));

varphi^2*theta__B*Lambda__p*alpha__B*Lambda__A/(mu__c*mu__A*N__p^2*(mu__A*mu__c+mu__A*omega__B+mu__A*sigma__B+mu__c*delta__A+delta__A*omega__B+delta__A*sigma__B))

(1)

#
# Compute "all" derivatives and evaluate numerically.
#
# For the purposes of this calculation "all"
# derivatives, means the derivatives with respect to
# every variable returned by indets(R, name)
#
# Output a list of two element lists where each of
# the latter is
#
# [ varName,
#   eval( diff( R, varName), params )
# ]
#
 [ seq( [j, eval( diff( R, j), params )],j in indets(R, name))];

Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received [Lambda__p = 100, gamma__B = 0.5e-1, gamma__B = 0.5e-1, gamma__C = 0.1e-1, omega__C = 0.1e-2, omega__B = 0.1e-2, sigma__B = 0.1e-3, sigma__C = 0.1e-1, sigma__BC = 0.1e-1, theta__B = .8, theta__C = .5, mu__C = 1.0, Lambda__A = 1.0, Lambda__w = 1.0, 33*varphi__8, mu__A = 1.0, mu__w = 1.0, alpha__B = 0.5e-2, alpha__C = 0.5e-2, alpha__BC = .15, Zeta__B = .5, Zeta__C = .5, delta__A = .66, delta__w = 1.33]

 

#
# Compute all "sensitivities" (where the sensitivity
# is as defined in Rouben Rostamian response to the
# OP's earlier post) and evaluate numerically.
#
# For the purposes of this calculation "all" sensitivities
# means the sensitivity with respect to every variable
# returned by indets(R, name)
#
# Output a list of two element lists where each of
# the latter is
#
# [ varName,
#   eval( varName*diff( R, varName)/R, params )
# ]
#
  seq( [j, eval( j*diff( R, j)/R, params )],j in indets(R, name));

Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received [Lambda__p = 100, gamma__B = 0.5e-1, gamma__B = 0.5e-1, gamma__C = 0.1e-1, omega__C = 0.1e-2, omega__B = 0.1e-2, sigma__B = 0.1e-3, sigma__C = 0.1e-1, sigma__BC = 0.1e-1, theta__B = .8, theta__C = .5, mu__C = 1.0, Lambda__A = 1.0, Lambda__w = 1.0, 33*varphi__8, mu__A = 1.0, mu__w = 1.0, alpha__B = 0.5e-2, alpha__C = 0.5e-2, alpha__BC = .15, Zeta__B = .5, Zeta__C = .5, delta__A = .66, delta__w = 1.33]

 

Download Computed_Sensitivity_Analys_for_CBD.mw

How can I import my data from my Ms word document to a Maple work sheet. Iam finding it difficult to save my work as a Dat file. Something like this example below

 

Data:=readdata("c:/Users/kokoge00/Desktop/methods.dat",float,10);
Data := [[0.1, 0.0769540597, 0.1477783335, 0.1393069312

  0.0763361154, 0.1477867626, 0.1393072151, 0.0763361266

  0.1477867830, 0.1393071934], [0.3, 0.1093424148, 0.1120401102

  0.1509302274, 0.1072278404, 0.1121142033, 0.1509369166

  0.1072278479, 0.1121142168, 0.1509369024], [0.5, 0.1392030568

  0.0853083077, 0.1558066181, 0.1353291378, 0.0855066806

  0.1558355785, 0.1353291558, 0.08550671332, 0.1558355439], [0.7, 

  0.1662374563, 0.0652194693, 0.1562235596, 0.1604342222

  0.0655908735, 0.1562974878, 0.1604342352, 0.06559089617, 

  0.1562974637], [0.9, 0.1903821623, 0.0500537619, 0.1537887672

  0.1825594352, 0.0506356391, 0.1539346707, 0.1825594528

  0.05063567192, 0.1539346352], [1.1, 0.2117168860, 0.0385555127

  0.1496220815, 0.2018541863, 0.0393727175, 0.1498707561

  0.2018542024, 0.03937274753, 0.1498707234], [1.3, 0.2303874000

  0.0298096396, 0.1444864012, 0.2185409755, 0.0308687065

  0.1448804021, 0.2185409880, 0.03086872986, 0.1448803765], [1.5, 

  0.2465077820, 0.0231661161, 0.1388614678, 0.2328759081

  0.0244336214, 0.1394893808, 0.2328759200, 0.02443364533, 

  0.1394893543]]
 

Please help with the bifurcation diagram for the system and parameter values below

NULL

with(VectorCalculus)

[`&x`, `*`, `+`, `-`, `.`, `<,>`, `<|>`, About, AddCoordinates, ArcLength, BasisFormat, Binormal, ConvertVector, CrossProduct, Curl, Curvature, D, Del, DirectionalDiff, Divergence, DotProduct, Flux, GetCoordinateParameters, GetCoordinates, GetNames, GetPVDescription, GetRootPoint, GetSpace, Gradient, Hessian, IsPositionVector, IsRootedVector, IsVectorField, Jacobian, Laplacian, LineInt, MapToBasis, Nabla, Norm, Normalize, PathInt, PlotPositionVector, PlotVector, PositionVector, PrincipalNormal, RadiusOfCurvature, RootedVector, ScalarPotential, SetCoordinateParameters, SetCoordinates, SpaceCurve, SurfaceInt, TNBFrame, TangentLine, TangentPlane, TangentVector, Torsion, Vector, VectorField, VectorPotential, VectorSpace, Wronskian, diff, eval, evalVF, int, limit, series]

(1)

interface(imaginaryunit = F)

I

(2)

M := Pi*theta-S*c__1-S*lambda+S__v*v__2

Pi*theta-S*c__1-S*lambda+S__v*v__2

(3)

Y := -S__v*c__2*lambda+Pi*b__1+S*v__1-S__v*c__3

-S__v*c__2*lambda+Pi*b__1+S*v__1-S__v*c__3

(4)

P := S__v*alpha+`&rho;__A`*A+c__4*`&rho;__Q`*Q+I*`&rho;__I`-µ*V

Q*c__4*rho__Q+A*rho__A+I*rho__I+S__v*alpha-V*µ

(5)

R := S__v*c__2*lambda-E*c__5+S*lambda

S__v*c__2*lambda-E*c__5+S*lambda

(6)

U := E*a*delta+Q*k*`&rho;__Q`-A*c__6

E*a*delta+Q*k*rho__Q-A*c__6

(7)

L := c__7*E-I*c__8

E*c__7-I*c__8

(8)

X := q__E*E+I*q__I-c__9*Q

E*q__E+I*q__I-Q*c__9

(9)

solve({L = 0, M = 0, P = 0, R = 0, U = 0, X = 0, Y = 0}, {I, A, E, Q, S, S__v, V})

{A = (a*c__8*c__9*delta+c__7*k*q__I*rho__Q+c__8*k*q__E*rho__Q)*lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__6*c__9*c__5*c__8*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), E = lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__5*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), I = c__7*lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__5*c__8*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), Q = (c__7*q__I+c__8*q__E)*lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__9*c__5*c__8*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), S = Pi*(c__2*lambda*theta+b__1*v__2+c__3*theta)/(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2), S__v = Pi*(b__1*c__1+b__1*lambda+theta*v__1)/(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2), V = Pi*(a*b__1*c__1*c__2*c__8*c__9*delta*lambda*rho__A+a*b__1*c__2*c__8*c__9*delta*lambda^2*rho__A+a*c__2*c__8*c__9*delta*lambda^2*rho__A*theta+a*c__2*c__8*c__9*delta*lambda*rho__A*theta*v__1+b__1*c__1*c__2*c__4*c__6*c__7*lambda*q__I*rho__Q+b__1*c__1*c__2*c__4*c__6*c__8*lambda*q__E*rho__Q+b__1*c__1*c__2*c__7*k*lambda*q__I*rho__A*rho__Q+b__1*c__1*c__2*c__8*k*lambda*q__E*rho__A*rho__Q+b__1*c__2*c__4*c__6*c__7*lambda^2*q__I*rho__Q+b__1*c__2*c__4*c__6*c__8*lambda^2*q__E*rho__Q+b__1*c__2*c__7*k*lambda^2*q__I*rho__A*rho__Q+b__1*c__2*c__8*k*lambda^2*q__E*rho__A*rho__Q+c__2*c__4*c__6*c__7*lambda^2*q__I*rho__Q*theta+c__2*c__4*c__6*c__7*lambda*q__I*rho__Q*theta*v__1+c__2*c__4*c__6*c__8*lambda^2*q__E*rho__Q*theta+c__2*c__4*c__6*c__8*lambda*q__E*rho__Q*theta*v__1+c__2*c__7*k*lambda^2*q__I*rho__A*rho__Q*theta+c__2*c__7*k*lambda*q__I*rho__A*rho__Q*theta*v__1+c__2*c__8*k*lambda^2*q__E*rho__A*rho__Q*theta+c__2*c__8*k*lambda*q__E*rho__A*rho__Q*theta*v__1+a*b__1*c__8*c__9*delta*lambda*rho__A*v__2+a*c__3*c__8*c__9*delta*lambda*rho__A*theta+b__1*c__1*c__2*c__6*c__7*c__9*lambda*rho__I+b__1*c__2*c__6*c__7*c__9*lambda^2*rho__I+b__1*c__4*c__6*c__7*lambda*q__I*rho__Q*v__2+b__1*c__4*c__6*c__8*lambda*q__E*rho__Q*v__2+b__1*c__7*k*lambda*q__I*rho__A*rho__Q*v__2+b__1*c__8*k*lambda*q__E*rho__A*rho__Q*v__2+c__2*c__6*c__7*c__9*lambda^2*rho__I*theta+c__2*c__6*c__7*c__9*lambda*rho__I*theta*v__1+c__3*c__4*c__6*c__7*lambda*q__I*rho__Q*theta+c__3*c__4*c__6*c__8*lambda*q__E*rho__Q*theta+c__3*c__7*k*lambda*q__I*rho__A*rho__Q*theta+c__3*c__8*k*lambda*q__E*rho__A*rho__Q*theta+alpha*b__1*c__1*c__5*c__6*c__8*c__9+alpha*b__1*c__5*c__6*c__8*c__9*lambda+alpha*c__5*c__6*c__8*c__9*theta*v__1+b__1*c__6*c__7*c__9*lambda*rho__I*v__2+c__3*c__6*c__7*c__9*lambda*rho__I*theta)/(c__5*c__6*c__8*c__9*µ*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2))}

(10)

``

lambda := beta*(I+`&eta;__A`*A+`&eta;__Q`*Q)/N

beta*(I+eta__A*A+eta__Q*Q)/N

(11)

``

NULL

k := .15

.15

(12)

delta := .125

.125

(13)

mu := 0.464360344e-4

0.464360344e-4

(14)

pi := .464360344

.464360344

(15)

delta__Q := 0.6847e-3

0.6847e-3

(16)

beta := .1086

.1086

(17)

q__E := 0.18113e-3

0.18113e-3

(18)

rho__Q := 0.815e-1

0.815e-1

(19)

a := .16255

.16255

(20)

v__1 := 0.5e-1

0.5e-1

(21)

v__2 := 0.5e-1

0.5e-1

(22)

alpha := 0.57e-1

0.57e-1

(23)

lambda := 0.765e-2

0.765e-2

(24)

rho__A := 0.915e-1

0.915e-1

(25)

rho__I := 0.515e-1

0.515e-1

(26)

a := .16255

.16255

(27)

q__I := 0.1923e-2

0.1923e-2

(28)

q__A := 0.4013e-7

0.4013e-7

(29)

eta__A := .1213

.1213

(30)

eta__Q := 0.3808e-2

0.3808e-2

(31)

w := .5925

.5925

(32)

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