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Yee Voon

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7 years, 273 days
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How to compute sensitivity analysis on b...

Yee Voon 20 Maple
sensitivity
March 04 2018
3 3

Basic_Reproduction_Number.mw
Hello, anybody knows how to compute sensitivity analysis for basic reproduction number using Maple coding? By taking the partial derivatives of all the parameters involved in the basic reproduction number using normalised forward sensitivity index formula. Thanks.

> 

restart
> 

unprotect(Pi)
> 

R[0] := k*tau*[(rho*(Upsilon*(mu+alpha+eta)+chi)+(1-rho)*(Upsilon*(1-q)*eta+mu+beta+chi))/((mu+beta+chi)*(mu+alpha+eta)-chi*eta*(1-q))]*(Pi*(-mu*p+mu+phi)/(mu*(vartheta+mu+phi))+epsilon*Pi*(mu*p+vartheta)/(mu*(vartheta+mu+phi)))

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

 (1)
> 

``


 

Download Basic_Reproduction_Number.mw

 

How to compute basic reproduction number...

Yee Voon 20 Maple
solve programming
February 06 2018
0 1

Does anyone know how to calculate basic reproduction number using maple coding? Or by any chance, anyone know how to solve it by hand with this complicated equations?
 

> 

restart
> 

interface(imaginaryunit = j)

I

 (1)
> 

lambda := k*tau*(C*Upsilon+I)/N

k*tau*(C*Upsilon+I)/N

 (2)
> 

eqn1 := (1-p)*Pi+phi*V+delta*R-(mu+lambda+`ϑ`)*S

(1-p)*Pi+phi*V+delta*R-(mu+k*tau*(C*Upsilon+I)/N+vartheta)*S

 (3)
> 

eqn2 := p*Pi+`ϑ`*S-(lambda*`ε`+mu+phi)*V

p*Pi+vartheta*S-(epsilon*k*tau*(C*Upsilon+I)/N+mu+phi)*V

 (4)
> 

eqn3 := rho*lambda*S+rho*`ε`*lambda*V+I*(1-q)*eta-(mu+beta+chi)*C

rho*k*tau*(C*Upsilon+I)*S/N+rho*epsilon*k*tau*(C*Upsilon+I)*V/N+(1-q)*eta*I-(mu+beta+chi)*C

 (5)
> 

eqn4 := (1-rho)*lambda*S+(1-rho)*`ε`*lambda*V+chi*C-I*(mu+alpha+eta)

(1-rho)*k*tau*(C*Upsilon+I)*S/N+(1-rho)*epsilon*k*tau*(C*Upsilon+I)*V/N+chi*C-(mu+alpha+eta)*I

 (6)
> 

eqn5 := beta*C+I*q*eta-(mu+delta)*R

beta*C+q*eta*I-(mu+delta)*R

 (7)
> 

``


 

Download Equation_for_basic_reproduction_number.mwEquation_for_basic_reproduction_number.mw

why my solutions lost?...

Yee Voon 20 Maple
solve
December 26 2017
2 2


I am trying to find for the equilibrium but why my solutions lost?

> 

restart
> 

interface(imaginaryunit = j);

I

 (1)
> 

unprotect(Pi)
> 

lambda := k*tau*(C*Upsilon+I)/N;

k*tau*(C*Upsilon+I)/N

 (2)
> 

eqn1 := (1-p)*Pi+phi*V+delta*R-(mu+lambda+vartheta)*S;

(1-p)*Pi+phi*V+delta*R-(mu+k*tau*(C*Upsilon+I)/N+vartheta)*S

 (3)
> 

eqn2 := p*Pi+vartheta*S-(epsilon*lambda+mu+phi)*V;

p*Pi+vartheta*S-(epsilon*k*tau*(C*Upsilon+I)/N+mu+phi)*V

 (4)
> 

eqn3 := rho*lambda*S+rho*epsilon*lambda*V+(1-q)*eta*I-(mu+beta+chi)*C;

rho*k*tau*(C*Upsilon+I)*S/N+rho*epsilon*k*tau*(C*Upsilon+I)*V/N+(1-q)*eta*I-(mu+beta+chi)*C

 (5)
> 

eqn4 := (1-rho)*lambda*S+(1-rho)*epsilon*lambda*V+chi*C-(mu+alpha+eta)*I;

(1-rho)*k*tau*(C*Upsilon+I)*S/N+(1-rho)*epsilon*k*tau*(C*Upsilon+I)*V/N+chi*C-(mu+alpha+eta)*I

 (6)
> 

eqn5 := beta*C+q*eta*I-(mu+delta)*R;

beta*C+q*eta*I-(mu+delta)*R

 (7)
> 

mu := 0.1e-1;

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-2

  

.2

  

11610

 (8)
> 

Equilibria := solve({eqn1 = 0, eqn2 = 0, eqn3 = 0, eqn4 = 0, eqn5 = 0}, {C, I, R, S, V});

Warning, solutions may have been lost

  

{C = 0., I = 0., R = 0., S = 5946.585366, V = 5663.414634}

 (9)
> 

``


 

Download Equilibria.mw
 

> 

restart
> 

interface(imaginaryunit = j);

I

 (1)
> 

unprotect(Pi)
> 

lambda := k*tau*(C*Upsilon+I)/N;

k*tau*(C*Upsilon+I)/N

 (2)
> 

eqn1 := (1-p)*Pi+phi*V+delta*R-(mu+lambda+vartheta)*S;

(1-p)*Pi+phi*V+delta*R-(mu+k*tau*(C*Upsilon+I)/N+vartheta)*S

 (3)
> 

eqn2 := p*Pi+vartheta*S-(epsilon*lambda+mu+phi)*V;

p*Pi+vartheta*S-(epsilon*k*tau*(C*Upsilon+I)/N+mu+phi)*V

 (4)
> 

eqn3 := rho*lambda*S+rho*epsilon*lambda*V+(1-q)*eta*I-(mu+beta+chi)*C;

rho*k*tau*(C*Upsilon+I)*S/N+rho*epsilon*k*tau*(C*Upsilon+I)*V/N+(1-q)*eta*I-(mu+beta+chi)*C

 (5)
> 

eqn4 := (1-rho)*lambda*S+(1-rho)*epsilon*lambda*V+chi*C-(mu+alpha+eta)*I;

(1-rho)*k*tau*(C*Upsilon+I)*S/N+(1-rho)*epsilon*k*tau*(C*Upsilon+I)*V/N+chi*C-(mu+alpha+eta)*I

 (6)
> 

eqn5 := beta*C+q*eta*I-(mu+delta)*R;

beta*C+q*eta*I-(mu+delta)*R

 (7)
> 

mu := 0.1e-1;

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-2

  

.2

  

11610

 (8)
> 

Equilibria := solve({eqn1 = 0, eqn2 = 0, eqn3 = 0, eqn4 = 0, eqn5 = 0}, {C, I, R, S, V});

Warning, solutions may have been lost

  

{C = 0., I = 0., R = 0., S = 5946.585366, V = 5663.414634}

 (9)
> 

``


 

Download Equilibria.mw

 

How to solve endemic equilibrium?...

Yee Voon 20 Maple
solve equilibrium
December 20 2017
2 12

Anybody have idea how to solve endemic equilibrium using maple? 

dS/dt=(1−p)π+φV+δR−(μ+λ+ϑ)S

dV/dt=pπ+ϑS−(μ+ϵλ+φ)V

dC/dt=ρλS+ρϵλV+(1−q)ηI−(μ+β+χ)C

dI/dt=(1−ρ)λS+(1−ρ)ϵλV+χC−(μ+α+η)I

dR/dt=βC+qηI−(μ+δ)R

 

Or solve by hand?

Coding for simultaneous equation...

Yee Voon 20 Maple
solve
December 01 2017
1 0

0=(1−p)π+φV+δR−(μ+λ+ϑ)S

0=pπ+ϑS−(μ+ϵλ+φ)V

0=ρλS+ρϵλV+(1−q)ηI−(μ+β+χ)C

0=(1−ρ)λS+(1−ρ)ϵλV+χC−(μ+α+η)I

0=βC+qηI−(μ+δ)R

Anybody know how to solve using coding for all the variable S,V,C,I,R

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