The behaviour of an epidemiological model

Abstract

In this work we study the next system: { S′=A−β(1+vI)SIE′=β(1+vI)SI−αEI′=αE−γIR′=γI $$\[\left\{ {\begin{array}{*{20}{l}}{S'}& = &{A - \beta \left( {1 + vI} \right)SI}\\{E'}& = &{\beta \left( {1 + vI} \right)SI - \alpha E}\\{I'}& = &{\alpha E - \gamma I}\\{R'}& = &{\gamma I}\end{array}} \right.\]$$ which is a SEIR model, where first of all the probability of disease transmission depend linear of the number of infectious. We also consider and study the behaviour of the system if the probability of disease transmission depend of two degree polinom of the number of infectious.