一种用于流行病建模的年龄结构扩散模型：李对称与精确解

The Diffusive Epidemic Process on Barabasi-Albert Networks

We present a modified diffusive epidemic process that has a finite threshold on scale-free graphs. The diffusive epidemic process describes the epidemic spreading in a non-sedentary population, and it is a reaction-diffusion process. In the diffusion stage, the individuals can jump between connected nodes, according to different diffusive rates for the infected and susceptible individuals. In the reaction stage, the contagion can happen if there is an infected individual sharing the same node, and infected individuals can spontaneously recover. Our main modification is to turn the number of in…

Global Stability of a Diffusive SEIR Epidemic Model with Distributed Delay

We study the global dynamics of a reaction-diffusion SEIR infection model with distributed delay and nonlinear incidence rate. The well-posedness of the proposed model is proved. By means of Lyapunov functionals, we show that the disease free equilibrium state is globally asymptotically stable when the basic reproduction number is less or equal than one, and that the disease endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than one. Numerical simulations are provided to illustrate the obtained theoretical results.

Finite symmetries in agent-based epidemic models

We present an algorithm which explores permutation symmetries to describe the time evolution of agent-based epidemic models. The main idea to improve computation times relies on restricting the stochastic process to one sector of the vector space, labeled by a single permutation eigenvalue. In this scheme, the transition matrix reduces to block diagonal form, enhancing computational performance.

Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods

We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the spatial movement and interactions of a population of susceptible, infected and recovered individuals. Thanks to this, the unphysical feature of instantaneous diffusive effects, which is typical of parabolic models, is removed. In particular, we formally show how such reaction-diffusion models are recovered in an appropriate diffusive limit. The kinetic transpor…

流行病SI(R)S模型中的标度对称性与参数约简

Scaling symmetries and parameter reduction in epidemic SI(R)S models

本文利用标度对称性对流行病SI(R)S模型进行参数约简，将10参数母模型归一化为Hethcote的2参数扩展模型，从而简化了地方病分岔与稳定性分析。

Symmetries and normalization in 3-compartment epidemic models I: The replacement number dynamics

As shown recently by the author, constant population SI(R)S models map to Hethcote's classic endemic model originally proposed in 1973. This unifies a whole class of models with up to 10 parameters, all being isomorphic to a simple 2-parameter master model for endemic bifurcation. In this work this procedure is extended to a 14-parameter SSISS Model, including social behavior parameters, a (diminished) susceptibility of the R-compartment and unbalanced constant per capita birth and death rates, thus covering many prominent models in the literature. Under mild conditions, in the dynamics for fr…