### PCR system

The PCR system [Verdière et al. (2014), Cantin et al. (2016)] is an attempt to model human behaviors
during catastrophic events. It is given by the following system of ODE.

\begin{equation*}
\begin{cases}
\dfrac{d r}{d t}=\gamma (t) q \left( 1-\dfrac{r}{r_m} \right) - (B_1+B_2)r + F(r,c)rc+ G (r,p) rp + s_1 c + s_2 p \\
\dfrac{d c}{d t} = B_1 r - F (r,c) rc + C_1 p - s_1 c - C_2 c - \varphi (t) c \left( 1-b\right) + H(c,p)c p \\
\dfrac{d p}{d t} = B_2 r - s_2 p - G (r,p)r p - C_1 p + C_2 c - H(c,p)cp \\
\dfrac{d q}{d t} = -\gamma (t) q \left( 1- \dfrac{r}{r_m} \right) \\
\dfrac{d b}{d t} = \varphi (t) c \left( 1- b \right)
\end{cases}
\end{equation*}

*Graphical model for the PCR system*

*Functions \(\gamma \) and \(\varphi \)*

You can make your own simulation of the model: just enter decimal numbers between \(0 \) and \(1 \) for the parameters below.

*After you have done your simulation, you can *
download
* the results.*

*Solution of the PCR system*

N. Verdière, V. Lanza, R. Charrier, E. Dubos-Paillard, C. Bertelle, and M.A. Aziz-Alaoui.
Mathematical modeling of human behaviors during catastrophic events.
In *ICCSA 2014*, 67–74. University, Le Havre, 2014. ↩

G. Cantin, N. Verdière, V. Lanza, R. Charrier, E. Dubos-Paillard, D. Provitolo, C. Bertelle, and M.A. Aziz-Alaoui.
Mathematical Modeling of Human Behaviors During Catastrophic Events: Stability and Bifurcations.
In *International Journal of Bifurcation and Chaos*, Volume 26, Issue 10, September 2016. ↩