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Measles

 

 

Measles
   
Discipline:  Epidemiology
Accession:  2014

 

 

 

Short description:

This is an epidemiology model, about the spread of deseas.
Assume a constant population represented by N and divided into 4 groups: susceptible, infectious, latent and immune individuals.

At time t those groups are S(t), I(t), L(t) and M(t). So:

S(t)+I(t)+L(t)+M(t)=N, \quad t \in [0,1]

Applicable solvers:

twpbvpc,twpbvplc,colsys,colnew,bvp_m2

 

Plots of the solution <- click to generate the plots of the solution and the textual output

 

Mathematical description:

\begin{array}{c} y_1' = \mu - \beta(t)y_1y_3 \\ y_2' = \beta(t)y_1 y_3-y_2 / \lambda \quad 0<t<1 \\ y_3'=y_2/\lambda-y_3 / \eta \end{array}{c}
with y_1=S/N, y_2=L/N, y_3=I/N, \beta(t)=\beta_0(1+cos 2\pi t)
and
\mu =0.02, \lambda=0.0279, \eta=0.01, \beta_0=1575

The boundary conditions are:
y(1)=y(0)

We can divide the boundary conditions with a vector of constants:
c=(c_1, c_2, c_3)^T 
Then:
c'=0, y(0)=c(0), \quad y(1)=c(1)

 

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References

 

U. M. Ascher. R.M.M. Mattheij and R. D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, SIAM, Philadelphia, 1995.