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
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