### 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.

### Simulation

 $B_1 =$ $C_1 =$ $s_1 =$ $\alpha_1 =$ $\delta_1 =$ $\mu_1 =$ $B_2 =$ $C_2 =$ $s_2 =$ $\alpha_2 =$ $\delta_2 =$ $\mu_2 =$

 Warning!!! You must enter decimal numbers between $0$ and $1$.

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

Solution of the PCR system

## Bibliography

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.