706 research outputs found
A Discrete-time Networked Competitive Bivirus SIS Model
The paper deals with the analysis of a discrete-time networked competitive
bivirus susceptible-infected-susceptible (SIS) model. More specifically, we
suppose that virus 1 and virus 2 are circulating in the population and are in
competition with each other. We show that the model is strongly monotone, and
that, under certain assumptions, it does not admit any periodic orbit. We
identify a sufficient condition for exponential convergence to the disease-free
equilibrium (DFE). Assuming only virus 1 (resp. virus 2) is alive, we establish
a condition for global asymptotic convergence to the single-virus endemic
equilibrium of virus 1 (resp. virus 2) -- our proof does not rely on the
construction of a Lyapunov function. Assuming both virus 1 and virus 2 are
alive, we establish a condition which ensures local exponential convergence to
the single-virus equilibrium of virus 1 (resp. virus 2). Finally, we provide a
sufficient (resp. necessary) condition for the existence of a coexistence
equilibrium
General SIS diffusion process with indirect spreading pathways on a hypergraph
While conventional graphs only characterize pairwise interactions,
higher-order networks (hypergraph, simplicial complex) capture multi-body
interactions, which is a potentially more suitable modeling framework for a
complex real system. However, the introduction of higher-order interactions
brings new challenges for the rigorous analysis of such systems on a
higher-order network. In this paper, we study a series of SIS-type diffusion
processes with both indirect and direct pathways on a directed hypergraph. In a
concrete case, the model we propose is based on a specific choice (polynomial)
of interaction function (how several agents influence each other when they are
in a hyperedge). Then, by the same choice of interaction function, we further
extend the system and propose a bi-virus competing model on a directed
hypergraph by coupling two single-virus models together. Finally, the most
general model in this paper considers an abstract interaction function under
single-virus and bi-virus settings. For the single-virus model, we provide the
results regarding healthy state and endemic equilibrium. For the bi-virus
setting, we further give an analysis of the existence and stability of the
healthy state, dominant endemic equilibria, and coexisting equilibria. All
theoretical results are finally supported by some numerical examples
A network SIS meta-population model with transportation flow
This paper considers a deterministic Susceptible-Infected-Susceptible (SIS) metapopulation model for the spread of a disease in a strongly connected network, where each node represents a large population. Individuals can travel between the nodes (populations). We derive a necessary and sufficient condition for the healthy equilibrium to be the unique equilibrium of the system, and then in fact it is asymptotically stable for all initial conditions (a sufficient condition for exponential stability is also given). If the condition is not satisfied, then there additionally exists a unique endemic equilibrium which is exponentially stable for all nonzero initial conditions. We then consider time-delay in the travel between nodes, and further investigate the role of the mobility rate that governs the flow of individuals between nodes in determining the convergence properties. We find that sometimes, increasing mobility helps the system converge to the healthy equilibrium.</p
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