Mixing
Drawing graphs of parametric equations
$begingroup$
the SIR model is an epidemiological model which sorts the whole population into three subclasses. x(t)(susceptibles), y(t)(infected), z(t)(recovered), with initial populations $x(0)= N_{1},y(0) = N_{2}, z(0)=N_{3}$
The solutions to the model are:
begin{equation}
x=x_{0}u
end{equation}
begin{equation}
y=-x_{0}+frac{gamma}{beta}ln u - frac{C_{1}}{beta}
end{equation}
begin{equation}
z = -frac{gamma}{beta}ln u
end{equation}
where $x_{0}, gamma ,C_{1} beta $ are arbitrary constants. And u is a function of time and it is equal to:
begin{equation}
u = e^{-frac{beta}{gamma}z}
end{equation}
For example
begin{equation}
u(0)=e^{-frac{beta}{gamma}N_{3}}
end{equation}
How would I graph the functions with time being the x axis and number of individuals represented on the y-axis?
calculus graphing-functions parametric biology
asked Jan 20 at 19:43
wittgensteinsrulerwittgensteinsruler
243
$endgroup$
add a comment |
$begingroup$
the SIR model is an epidemiological model which sorts the whole population into three subclasses. x(t)(susceptibles), y(t)(infected), z(t)(recovered), with initial populations $x(0)= N_{1},y(0) = N_{2}, z(0)=N_{3}$
The solutions to the model are:
begin{equation}
x=x_{0}u
end{equation}
begin{equation}
y=-x_{0}+frac{gamma}{beta}ln u - frac{C_{1}}{beta}
end{equation}
begin{equation}
z = -frac{gamma}{beta}ln u
end{equation}
where $x_{0}, gamma ,C_{1} beta $ are arbitrary constants. And u is a function of time and it is equal to:
begin{equation}
u = e^{-frac{beta}{gamma}z}
end{equation}
For example
begin{equation}
u(0)=e^{-frac{beta}{gamma}N_{3}}
end{equation}
How would I graph the functions with time being the x axis and number of individuals represented on the y-axis?
calculus graphing-functions parametric biology
asked Jan 20 at 19:43
wittgensteinsrulerwittgensteinsruler
243
$endgroup$
add a comment |
$begingroup$
the SIR model is an epidemiological model which sorts the whole population into three subclasses. x(t)(susceptibles), y(t)(infected), z(t)(recovered), with initial populations $x(0)= N_{1},y(0) = N_{2}, z(0)=N_{3}$
The solutions to the model are:
begin{equation}
x=x_{0}u
end{equation}
begin{equation}
y=-x_{0}+frac{gamma}{beta}ln u - frac{C_{1}}{beta}
end{equation}
begin{equation}
z = -frac{gamma}{beta}ln u
end{equation}
where $x_{0}, gamma ,C_{1} beta $ are arbitrary constants. And u is a function of time and it is equal to:
begin{equation}
u = e^{-frac{beta}{gamma}z}
end{equation}
For example
begin{equation}
u(0)=e^{-frac{beta}{gamma}N_{3}}
end{equation}
How would I graph the functions with time being the x axis and number of individuals represented on the y-axis?
calculus graphing-functions parametric biology
asked Jan 20 at 19:43
wittgensteinsrulerwittgensteinsruler
243
$endgroup$
the SIR model is an epidemiological model which sorts the whole population into three subclasses. x(t)(susceptibles), y(t)(infected), z(t)(recovered), with initial populations $x(0)= N_{1},y(0) = N_{2}, z(0)=N_{3}$
The solutions to the model are:
begin{equation}
x=x_{0}u
end{equation}
begin{equation}
y=-x_{0}+frac{gamma}{beta}ln u - frac{C_{1}}{beta}
end{equation}
begin{equation}
z = -frac{gamma}{beta}ln u
end{equation}
where $x_{0}, gamma ,C_{1} beta $ are arbitrary constants. And u is a function of time and it is equal to:
begin{equation}
u = e^{-frac{beta}{gamma}z}
end{equation}
For example
begin{equation}
u(0)=e^{-frac{beta}{gamma}N_{3}}
end{equation}
How would I graph the functions with time being the x axis and number of individuals represented on the y-axis?
calculus graphing-functions parametric biology
calculus graphing-functions parametric biology
asked Jan 20 at 19:43
wittgensteinsrulerwittgensteinsruler
243
asked Jan 20 at 19:43
wittgensteinsrulerwittgensteinsruler
243
asked Jan 20 at 19:43
wittgensteinsrulerwittgensteinsruler
243
asked Jan 20 at 19:43
wittgensteinsrulerwittgensteinsruler
243
asked Jan 20 at 19:43
wittgensteinsrulerwittgensteinsruler
243
243
add a comment |
add a comment |
1 Answer
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I would suggest numerically solving the original ordinary system of differential equations (that gives rise to the parametrized solution of the SIR model). This is the easiest way to plot the variable over time.
answered Feb 13 at 22:47
PaichuPaichu
771616
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
I would suggest numerically solving the original ordinary system of differential equations (that gives rise to the parametrized solution of the SIR model). This is the easiest way to plot the variable over time.
answered Feb 13 at 22:47
PaichuPaichu
771616
$endgroup$
add a comment |
$begingroup$
I would suggest numerically solving the original ordinary system of differential equations (that gives rise to the parametrized solution of the SIR model). This is the easiest way to plot the variable over time.
answered Feb 13 at 22:47
PaichuPaichu
771616
$endgroup$
add a comment |
$begingroup$
I would suggest numerically solving the original ordinary system of differential equations (that gives rise to the parametrized solution of the SIR model). This is the easiest way to plot the variable over time.
answered Feb 13 at 22:47
PaichuPaichu
771616
$endgroup$
I would suggest numerically solving the original ordinary system of differential equations (that gives rise to the parametrized solution of the SIR model). This is the easiest way to plot the variable over time.
answered Feb 13 at 22:47
PaichuPaichu
771616
answered Feb 13 at 22:47
PaichuPaichu
771616
answered Feb 13 at 22:47
PaichuPaichu
771616
answered Feb 13 at 22:47
PaichuPaichu
771616
771616
add a comment |
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