Solving system of nonlinear differential equation in MAPLE












0












$begingroup$


I'am working out on nonlinear differential equation and I need to find the equilibrium point which means all the system is equal to zero.
Here is the System of Diferential Equation:



begin{align*}
frac{dS}{dt} &= alpha - beta SV - delta S \
frac{dI}{dt} &= beta SV - sigma I \
frac{dV}{dt} &= mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV
end{align*}



then, to find the equilibrium point set $frac{dS}{dt} = frac{dI}{dI} = frac{dV}{dt} = 0$. It means that I have to solve the system of equation
begin{align*}
alpha - beta SV - delta S &=0 \
beta SV - sigma I &= 0\
mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV &=0
end{align*}



I've got the result by solving it manually but Can I use MAPLE software to solve this problem?



What I've done manually:
$V = frac{alpha - delta S}{beta S}, I = frac{alpha - delta S}{sigma}, S = frac{alpha}{delta} text{ or } S = frac{(gamma_1 +gamma_2+gamma_3)sigma}{beta(mu n - sigma)} $






maple







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$endgroup$












  • $begingroup$
    What result have you got?
    $endgroup$
    – Dr. Sonnhard Graubner
    Dec 22 '18 at 11:50










  • $begingroup$
    I've made some changes to my post @Dr.SonnhardGraubner
    $endgroup$
    – SutMar
    Dec 22 '18 at 12:06










  • $begingroup$
    I have solved it with Maple and now?
    $endgroup$
    – Dr. Sonnhard Graubner
    Dec 22 '18 at 12:29










  • $begingroup$
    I will feel happy if you are willing to teach it to me.
    $endgroup$
    – SutMar
    Dec 22 '18 at 13:04
















0












$begingroup$


I'am working out on nonlinear differential equation and I need to find the equilibrium point which means all the system is equal to zero.
Here is the System of Diferential Equation:



begin{align*}
frac{dS}{dt} &= alpha - beta SV - delta S \
frac{dI}{dt} &= beta SV - sigma I \
frac{dV}{dt} &= mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV
end{align*}



then, to find the equilibrium point set $frac{dS}{dt} = frac{dI}{dI} = frac{dV}{dt} = 0$. It means that I have to solve the system of equation
begin{align*}
alpha - beta SV - delta S &=0 \
beta SV - sigma I &= 0\
mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV &=0
end{align*}



I've got the result by solving it manually but Can I use MAPLE software to solve this problem?



What I've done manually:
$V = frac{alpha - delta S}{beta S}, I = frac{alpha - delta S}{sigma}, S = frac{alpha}{delta} text{ or } S = frac{(gamma_1 +gamma_2+gamma_3)sigma}{beta(mu n - sigma)} $






maple







share|cite|improve this question











$endgroup$












  • $begingroup$
    What result have you got?
    $endgroup$
    – Dr. Sonnhard Graubner
    Dec 22 '18 at 11:50










  • $begingroup$
    I've made some changes to my post @Dr.SonnhardGraubner
    $endgroup$
    – SutMar
    Dec 22 '18 at 12:06










  • $begingroup$
    I have solved it with Maple and now?
    $endgroup$
    – Dr. Sonnhard Graubner
    Dec 22 '18 at 12:29










  • $begingroup$
    I will feel happy if you are willing to teach it to me.
    $endgroup$
    – SutMar
    Dec 22 '18 at 13:04














0












0








0





$begingroup$


I'am working out on nonlinear differential equation and I need to find the equilibrium point which means all the system is equal to zero.
Here is the System of Diferential Equation:



begin{align*}
frac{dS}{dt} &= alpha - beta SV - delta S \
frac{dI}{dt} &= beta SV - sigma I \
frac{dV}{dt} &= mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV
end{align*}



then, to find the equilibrium point set $frac{dS}{dt} = frac{dI}{dI} = frac{dV}{dt} = 0$. It means that I have to solve the system of equation
begin{align*}
alpha - beta SV - delta S &=0 \
beta SV - sigma I &= 0\
mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV &=0
end{align*}



I've got the result by solving it manually but Can I use MAPLE software to solve this problem?



What I've done manually:
$V = frac{alpha - delta S}{beta S}, I = frac{alpha - delta S}{sigma}, S = frac{alpha}{delta} text{ or } S = frac{(gamma_1 +gamma_2+gamma_3)sigma}{beta(mu n - sigma)} $






maple







share|cite|improve this question











$endgroup$




I'am working out on nonlinear differential equation and I need to find the equilibrium point which means all the system is equal to zero.
Here is the System of Diferential Equation:



begin{align*}
frac{dS}{dt} &= alpha - beta SV - delta S \
frac{dI}{dt} &= beta SV - sigma I \
frac{dV}{dt} &= mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV
end{align*}



then, to find the equilibrium point set $frac{dS}{dt} = frac{dI}{dI} = frac{dV}{dt} = 0$. It means that I have to solve the system of equation
begin{align*}
alpha - beta SV - delta S &=0 \
beta SV - sigma I &= 0\
mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV &=0
end{align*}



I've got the result by solving it manually but Can I use MAPLE software to solve this problem?



What I've done manually:
$V = frac{alpha - delta S}{beta S}, I = frac{alpha - delta S}{sigma}, S = frac{alpha}{delta} text{ or } S = frac{(gamma_1 +gamma_2+gamma_3)sigma}{beta(mu n - sigma)} $






maple




maple






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share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 22 '18 at 12:05







SutMar

















asked Dec 22 '18 at 11:42









SutMarSutMar

1007




1007












  • $begingroup$
    What result have you got?
    $endgroup$
    – Dr. Sonnhard Graubner
    Dec 22 '18 at 11:50










  • $begingroup$
    I've made some changes to my post @Dr.SonnhardGraubner
    $endgroup$
    – SutMar
    Dec 22 '18 at 12:06










  • $begingroup$
    I have solved it with Maple and now?
    $endgroup$
    – Dr. Sonnhard Graubner
    Dec 22 '18 at 12:29










  • $begingroup$
    I will feel happy if you are willing to teach it to me.
    $endgroup$
    – SutMar
    Dec 22 '18 at 13:04


















  • $begingroup$
    What result have you got?
    $endgroup$
    – Dr. Sonnhard Graubner
    Dec 22 '18 at 11:50










  • $begingroup$
    I've made some changes to my post @Dr.SonnhardGraubner
    $endgroup$
    – SutMar
    Dec 22 '18 at 12:06










  • $begingroup$
    I have solved it with Maple and now?
    $endgroup$
    – Dr. Sonnhard Graubner
    Dec 22 '18 at 12:29










  • $begingroup$
    I will feel happy if you are willing to teach it to me.
    $endgroup$
    – SutMar
    Dec 22 '18 at 13:04
















$begingroup$
What result have you got?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 11:50




$begingroup$
What result have you got?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 11:50












$begingroup$
I've made some changes to my post @Dr.SonnhardGraubner
$endgroup$
– SutMar
Dec 22 '18 at 12:06




$begingroup$
I've made some changes to my post @Dr.SonnhardGraubner
$endgroup$
– SutMar
Dec 22 '18 at 12:06












$begingroup$
I have solved it with Maple and now?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 12:29




$begingroup$
I have solved it with Maple and now?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 12:29












$begingroup$
I will feel happy if you are willing to teach it to me.
$endgroup$
– SutMar
Dec 22 '18 at 13:04




$begingroup$
I will feel happy if you are willing to teach it to me.
$endgroup$
– SutMar
Dec 22 '18 at 13:04










1 Answer
1






active

oldest

votes


















2












$begingroup$

Here is how to do it in Maple



eqs:={alpha-beta*S*V-delta*S,beta*S*V-sigma*II,
mu*n*II-gamma[1]*V-gamma[2]*V-gamma[3]*V-beta*S*V};
vars:={S,II,V};
solve(eqs,vars);



Note that I is a reserved symbol in Maple, so I just used another symbol II for it.



Maple yields two solutions
$$
left{ {it II}=0,S={frac {alpha}{delta}},V=0 right}
$$
and
$$
left{ {it II}={frac {alpha,beta,mu,n-alpha,beta,sigma-
delta,sigma,gamma_{{1}}-delta,sigma,gamma_{{2}}-delta,
sigma,gamma_{{3}}}{beta,sigma, left( mu,n-sigma right) }},
S={frac {sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}}
right) }{beta, left( mu,n-sigma right) }},
\
V={frac {alpha,
beta,mu,n-alpha,beta,sigma-delta,sigma,gamma_{{1}}-
delta,sigma,gamma_{{2}}-delta,sigma,gamma_{{3}}}{beta,
sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}} right) }}
right}
$$






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    1 Answer
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    1 Answer
    1






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    $begingroup$

    Here is how to do it in Maple



    eqs:={alpha-beta*S*V-delta*S,beta*S*V-sigma*II,
    mu*n*II-gamma[1]*V-gamma[2]*V-gamma[3]*V-beta*S*V};
    vars:={S,II,V};
    solve(eqs,vars);



    Note that I is a reserved symbol in Maple, so I just used another symbol II for it.



    Maple yields two solutions
    $$
    left{ {it II}=0,S={frac {alpha}{delta}},V=0 right}
    $$
    and
    $$
    left{ {it II}={frac {alpha,beta,mu,n-alpha,beta,sigma-
    delta,sigma,gamma_{{1}}-delta,sigma,gamma_{{2}}-delta,
    sigma,gamma_{{3}}}{beta,sigma, left( mu,n-sigma right) }},
    S={frac {sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}}
    right) }{beta, left( mu,n-sigma right) }},
    \
    V={frac {alpha,
    beta,mu,n-alpha,beta,sigma-delta,sigma,gamma_{{1}}-
    delta,sigma,gamma_{{2}}-delta,sigma,gamma_{{3}}}{beta,
    sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}} right) }}
    right}
    $$






    share|cite|improve this answer









    $endgroup$


















      2












      $begingroup$

      Here is how to do it in Maple



      eqs:={alpha-beta*S*V-delta*S,beta*S*V-sigma*II,
      mu*n*II-gamma[1]*V-gamma[2]*V-gamma[3]*V-beta*S*V};
      vars:={S,II,V};
      solve(eqs,vars);



      Note that I is a reserved symbol in Maple, so I just used another symbol II for it.



      Maple yields two solutions
      $$
      left{ {it II}=0,S={frac {alpha}{delta}},V=0 right}
      $$
      and
      $$
      left{ {it II}={frac {alpha,beta,mu,n-alpha,beta,sigma-
      delta,sigma,gamma_{{1}}-delta,sigma,gamma_{{2}}-delta,
      sigma,gamma_{{3}}}{beta,sigma, left( mu,n-sigma right) }},
      S={frac {sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}}
      right) }{beta, left( mu,n-sigma right) }},
      \
      V={frac {alpha,
      beta,mu,n-alpha,beta,sigma-delta,sigma,gamma_{{1}}-
      delta,sigma,gamma_{{2}}-delta,sigma,gamma_{{3}}}{beta,
      sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}} right) }}
      right}
      $$






      share|cite|improve this answer









      $endgroup$
















        2












        2








        2





        $begingroup$

        Here is how to do it in Maple



        eqs:={alpha-beta*S*V-delta*S,beta*S*V-sigma*II,
        mu*n*II-gamma[1]*V-gamma[2]*V-gamma[3]*V-beta*S*V};
        vars:={S,II,V};
        solve(eqs,vars);



        Note that I is a reserved symbol in Maple, so I just used another symbol II for it.



        Maple yields two solutions
        $$
        left{ {it II}=0,S={frac {alpha}{delta}},V=0 right}
        $$
        and
        $$
        left{ {it II}={frac {alpha,beta,mu,n-alpha,beta,sigma-
        delta,sigma,gamma_{{1}}-delta,sigma,gamma_{{2}}-delta,
        sigma,gamma_{{3}}}{beta,sigma, left( mu,n-sigma right) }},
        S={frac {sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}}
        right) }{beta, left( mu,n-sigma right) }},
        \
        V={frac {alpha,
        beta,mu,n-alpha,beta,sigma-delta,sigma,gamma_{{1}}-
        delta,sigma,gamma_{{2}}-delta,sigma,gamma_{{3}}}{beta,
        sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}} right) }}
        right}
        $$






        share|cite|improve this answer









        $endgroup$



        Here is how to do it in Maple



        eqs:={alpha-beta*S*V-delta*S,beta*S*V-sigma*II,
        mu*n*II-gamma[1]*V-gamma[2]*V-gamma[3]*V-beta*S*V};
        vars:={S,II,V};
        solve(eqs,vars);



        Note that I is a reserved symbol in Maple, so I just used another symbol II for it.



        Maple yields two solutions
        $$
        left{ {it II}=0,S={frac {alpha}{delta}},V=0 right}
        $$
        and
        $$
        left{ {it II}={frac {alpha,beta,mu,n-alpha,beta,sigma-
        delta,sigma,gamma_{{1}}-delta,sigma,gamma_{{2}}-delta,
        sigma,gamma_{{3}}}{beta,sigma, left( mu,n-sigma right) }},
        S={frac {sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}}
        right) }{beta, left( mu,n-sigma right) }},
        \
        V={frac {alpha,
        beta,mu,n-alpha,beta,sigma-delta,sigma,gamma_{{1}}-
        delta,sigma,gamma_{{2}}-delta,sigma,gamma_{{3}}}{beta,
        sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}} right) }}
        right}
        $$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 22 '18 at 13:08









        GEdgarGEdgar

        62.7k267171




        62.7k267171






























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