We study a fast-slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
The classical Lanchester’s model is shortly reviewed and analysed, with particular attention to the critical issues that intrinsically arise from the mathematical formalization of the problem. We then generalize a particular version of such a model describing the dynamics of warfare when three or more armies are involved in the conflict. Several numerical simulations are provided.
We investigate time scale separation in the vector borne disease model
SIRUV, as previously described in the literature [1], and recently reanalyzed with the singular perturbation technique [2]. We focus on the analysis with a single small parameter, the birth and death rate μ, whereas all other model parameters are much larger and describe fast transitions.
The scaling of the endemic stationary state, the Jacobian matrix around
it and its eigenvalues with this small parameter μ is calculated and the
center manifold analysis performed with the method described in [3] which
goes back to earlier work [4, 5], namely a transformation of the Jacobian
matrix to block structure in zeroth order in the parameter μ is used and
then a family of center manifolds with μ larger than zero is obtained.
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