📂Dynamics

Lagrangian Motion Model

Definition ¹

The meta-population model that deals with short-term interactions between groups is called the Eulerian Movement Model.

Example

Let’s consider an extension of a simple SIR model. There are two patches, a home location $1$ and a vacation spot $2$, and the model that describes diseases that couldn’t possibly originate from the home location but are brought in from the vacation spot can be represented as a coupled dynamic system. $${{ d S_{1} } \over { dt }} = - \beta_{11} S_{1} I_{1} - \beta_{12} S_{1} I_{2}$$

Here, $\beta_{11}$ is the infection rate in the home location, and $\beta_{12}$ is the infection rate among the population that went on vacation to the vacation spot. Typically, in research, these are not constants but functions dependent on time $t$, which would be reasonably defined or derived based on real data. As it reflects temporary contact rather than permanent movement, it is also called a Simple Trip Model in the context of infectious disease models.