In the case of those susceptible, the process of generating latent people in the SEIR model is equivalent to that of creating infected in the SIR model. Therefore in this case the equation that describes the susceptible is the same in both models:

equation

In the case of the equation of latent cases, one must first consider those that have been infected and that the SIR model led to those infected\\n\\n

$-\displaystyle\frac{\beta C}{N} I(t) S(t $

\\n\\nwhere \beta is the probability of infected, C the number of contacts, S the number of those susceptible, I the number of those infected and N the number of the population.\\n\\nThe number of latents will decrease depending on the fraction \sigma that will show the symptoms and be part of those infected with symptoms I\\n\\n

$-\sigma E(t)$

\\n\\nSimilarly those who die from another cause should be considered\\n\\n

$-\mu_d E(t)$

so the equation to describe the latent will be

equation

In the case of the equation of infected cases, first consider those that are latent E and that in the proportion \sigma become infected

\sigma E(t)

The number of infected will decrease depending on the \gamma fraction of the infected I that is recovered

-\gamma I(t)

Similarly those who die from another cause should be considered

-\mu_d I(t)

so the equation to describe the infected will be

equation

In the case of the equation of recovered cases, it is necessary to first consider those that are infected I and that in the proportion \gamma become recovered\\n\\n

$\gamma I(t)$

\\n\\nSimilarly those who die from another cause should be considered\\n\\n

$-\mu_d R(t)$

so the equation to describe the infected will be

equation

If the probability of becoming infected is \beta, the number of contacts C, the reproduction factor \gamma, the step factor from latent to infected and \mu_d the death factor from other causes, the reproduction factor is

equation

In the critical case where the system becomes stable the number of latex E will not vary

equation=4087

and the infected I

equation=4088

where S is the number of susceptible, \beta is the probability of infecting, C number of contacts, N population number, \gamma is the recovery factor, \mu_b the birth factor and \mu_d the death factor.

The number of critical latents can be cleared from the second equation

equation=4092

If this value is replaced in the first equation, the critical value for the susceptible ones is obtained

equation

which corresponds to the situation in which the infected curve reaches its maximum. In other words, the number of critically susceptible is the number of susceptible that remain at the moment that the number of infected reaches its maximum.

From the equation of the infected I

equation=4088

where \gamma is the recovery factor, \sigma the latent to infected step factor, E the latent ones and \mu_d the factor of the dead.

As the number of susceptible in the critical case is

equation=4091

you can calculate the critical number of those infected

equation

which corresponds to the situation in which the infected curve reaches its maximum. In other words, the number of critical latents is the number of latents that remain at the moment that the number of infected reaches its maximum.

From the equation of the susceptible S

equation=4086

where \beta is the probability of infection, C the number of contacts, N the number of the population, I those infected, \mu_b the factor of births and \mu_d the factor of the dead.

As the number of susceptible in the asymptotic case is

equation=4090

the asymptotic number of those infected can be calculated

equation

In the case of SEIR models there are four curves, that of susceptible, latent, infected and recovered:

image

The model can solve numerically the equations for susceptible S, infected I, latent E and recovered R:

equation=4086

equation=4087

equation=4088

equation=4089

where t is the time \beta the cup of contagion, \sigma the cup of emergence of the symptoms in the infected, \gamma the recovery rate, C the number of contacts, N the population, \mu_b per capita birth rate and \mu_d per capita mortality.