Author: Constanze Ciavarella @ConniCia
Date: 2018-10-02
This code combines two deterministic metapopulation SEIR models as described in Lloyd & Jansen (2004).
Cross-coupling is controlled through matrix
Setting the off-diagonal elements of
Matrix
Setting all elements of
This model consists of many SEIR models connected through between-patch contact and/or migration of individuals between patches. The model has a constant total population size, which means that births and deaths correspond at each time step.
-
$n$ = number of patches -
$S_1, ..., S_n$ = susceptibles in patches$1, ..., n$ -
$E_1, ..., E_n$ = exposed in patches$1, ..., n$ -
$I_1, ..., I_n$ = infectious in patches$1, ..., n$ -
$R_1, ..., R_n$ = recovered in patches$1, ..., n$ -
$\beta_{ij}$ = effective contact rate of infected individuals of patch$i$ to susceptible individuals of patch$j$ -
$c_{ii}$ = outflow of patch$i$ -
$c_{ij}, i \neq j$ = flow from patch$i$ to patch$j$ -
$\sigma$ = rate of breakdown to active (and infectious) disease -
$\gamma$ = rate of recovery from active disease -
$\mu$ = background mortality/birth rate
The model will be written as $$ \begin{aligned} &S_i' = \mu - \mu S_i - S_i , \sum_{j=1}^n , \beta_{ij} , I_j + , m_S * (S_1 * c_{1i} , + ... + , S_n * c_{ni})\ &E_i' = S_i \sum_{j=1}^n \beta_{ij} , I_j - (\mu + \sigma) , E_i + , m_E * (E_1 * c_{1i} , + ... + , E_n * c_{ni})\ &I_i' = \sigma , E_i - (\mu + \gamma) , I_i + , m_I * (I_1 * c_{1i} , + ... + , I_n * c_{ni})\ &R_i' = \gamma , I_i - \mu , R_i + , m_R * (R_1 * c_{1i} , + ... + , R_n * c_{ni}) \end{aligned} $$