The SEIR Model
For many important infections there is a significant period of time during which the individual has been infected but is not yet infectious themselves. During this latent period the individual is in compartment E (for exposed).
Assuming that the period of staying in the latent state is a random variable with exponential distribution with parameter a (i.e. the average latent period is ), and also assuming the presence of vital dynamics with birth rate equal to death rate, we have the model:
Of course, we have that .
For this model, the basic reproduction number is:
Similarly to the SIR model, also in this case we have a Disease-Free-Equilibrium (N,0,0,0) and an Endemic Equilibrium EE, and one can show that, independently form biologically meaningful initial conditions
it holds that:
In case of periodically varying contact rate the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:
is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).
Read more about this topic: Compartmental Models In Epidemiology
Famous quotes containing the word model:
“AIDS occupies such a large part in our awareness because of what it has been taken to represent. It seems the very model of all the catastrophes privileged populations feel await them.”
—Susan Sontag (b. 1933)