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A SIS model with propagation of conducts
##manager.scheduler.building##: Edificio Santa Maria
##manager.scheduler.room##: Auditorio San Agustin
Date: 2019-07-10 12:00 PM – 03:45 PM
Last modified: 2019-06-14
Abstract
We modify a classical SIS model adding an opinion formation dynamic. The state of an agent $a_i$ is described as a couple $(\eta_i, p_i)$ where $\eta\in \{S,I\}$ describes the agent health state and $p\in[0,1]$ her protection measures. Briefly, if $\alpha$ and
$\beta$ are the infection and recovery rates, a susceptible agent with a protection level $p$ is infected after an interaction with an infected agent with probablity $(1-p)\alpha$. After an interaction, the levels of protection are increased or decreased depending on the existence of contagion or not.
The distribution of agents in $[0,1]$ is given by some measure $f$, and we obtain a Boltzmann-type equation describing its evolution, with a collision term depending on the proportion of infected agents. Also, a classical ordinary differential equation
depending on the mean value of $f$ gives the evolution of the proportion of infected agents.We simulated the discrete model and analyzed theoretically the results, obtaining the stationary states and showing the convergence to them depending only on $\alpha$ and $\beta$, and we find a transition between non-endemic and endemic behavior of the disease. By adding a media or Governement agent impulsing higher levels of protection it is possible to erradicate the endemic phase.
$\beta$ are the infection and recovery rates, a susceptible agent with a protection level $p$ is infected after an interaction with an infected agent with probablity $(1-p)\alpha$. After an interaction, the levels of protection are increased or decreased depending on the existence of contagion or not.
The distribution of agents in $[0,1]$ is given by some measure $f$, and we obtain a Boltzmann-type equation describing its evolution, with a collision term depending on the proportion of infected agents. Also, a classical ordinary differential equation
depending on the mean value of $f$ gives the evolution of the proportion of infected agents.We simulated the discrete model and analyzed theoretically the results, obtaining the stationary states and showing the convergence to them depending only on $\alpha$ and $\beta$, and we find a transition between non-endemic and endemic behavior of the disease. By adding a media or Governement agent impulsing higher levels of protection it is possible to erradicate the endemic phase.