3,267 research outputs found
Distributed interaction between computer virus and patch: A modeling study
The decentralized patch distribution mechanism holds significant promise as
an alternative to its centralized counterpart. For the purpose of accurately
evaluating the performance of the decentralized patch distribution mechanism
and based on the exact SIPS model that accurately captures the average dynamics
of the interaction between viruses and patches, a new virus-patch interacting
model, which is known as the generic SIPS model, is proposed. This model
subsumes the linear SIPS model. The dynamics of the generic SIPS model is
studied comprehensively. In particular, a set of criteria for the final
extinction or/and long-term survival of viruses or/and patches are presented.
Some conditions for the linear SIPS model to accurately capture the average
dynamics of the virus-patch interaction are empirically found. As a
consequence, the linear SIPS model can be adopted as a standard model for
assessing the performance of the distributed patch distribution mechanism,
provided the proper conditions are satisfied
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
Towards Understanding the Endemic Behavior of a Competitive Tri-Virus SIS Networked Model
This paper studies the endemic behavior of a multi-competitive networked
susceptible-infected-susceptible (SIS) model. Specifically, the paper deals
with three competing virus systems (i.e., tri-virus systems). First, we show
that a tri-virus system, unlike a bi-virus system, is not a monotone dynamical
system. Using the Parametric Transversality Theorem, we show that, generically,
a tri-virus system has a finite number of equilibria and that the Jacobian
matrices associated with each equilibrium are nonsingular. The endemic
equilibria of this system can be classified as follows: a) single-virus endemic
equilibria (also referred to as the boundary equilibria), where precisely one
of the three viruses is alive; b) 2-coexistence equilibria, where exactly two
of the three viruses are alive; and c) 3-coexistence equilibria, where all
three viruses survive in the network. We provide a necessary and sufficient
condition that guarantees local exponential convergence to a boundary
equilibrium. Further, we secure conditions for the nonexistence of
3-coexistence equilibria (resp. for various forms of 2-coexistence equilibria).
We also identify sufficient conditions for the existence of a 2-coexistence
(resp. 3-coexistence) equilibrium. We identify conditions on the model
parameters that give rise to a continuum of coexistence equilibria. More
specifically, we establish i) a scenario that admits the existence and local
exponential attractivity of a line of coexistence equilibria; and ii) scenarios
that admit the existence of, and, in the case of one such scenario, global
convergence to, a plane of 3-coexistence equilibria.Comment: arXiv admin note: substantial text overlap with arXiv:2209.1182
Competitive Networked Bivirus SIS spread over Hypergraphs
The paper deals with the spread of two competing viruses over a network of
population nodes, accounting for pairwise interactions and higher-order
interactions (HOI) within and between the population nodes. We study the
competitive networked bivirus susceptible-infected-susceptible (SIS) model on a
hypergraph introduced in Cui et al. [1]. We show that the system has, in a
generic sense, a finite number of equilibria, and the Jacobian associated with
each equilibrium point is nonsingular; the key tool is the Parametric
Transversality Theorem of differential topology. Since the system is also
monotone, it turns out that the typical behavior of the system is convergence
to some equilibrium point. Thereafter, we exhibit a tri-stable domain with
three locally exponentially stable equilibria. For different parameter regimes,
we establish conditions for the existence of a coexistence equilibrium (both
viruses infect separate fractions of each population node)
On a bi-virus epidemic model with partial and waning immunity
We propose a deterministic compartmental model to study the impact of partial and waning immunity on the spread of two competitive epidemic diseases, hereafter termed viruses. Building on a standard bi-virus SIS model, we introduce additional compartments to account for individuals who recovered from each virus, and tunable parameters to capture the level of virus-specific and cross protection acquired after recovery from a specific virus, and the rate at which such immunity could wane. We formalise the model as a system of nonlinear ordinary differential equations, which is amenable to analytical treatment, and we focus our analysis on two specialisations of the model. First, in the absence of waning immunity, we establish a global convergence result showing that, above the epidemic threshold, only the “fittest” virus becomes endemic. Second, in the absence of cross-immunity, we demonstrate instead that long-lasting co-existence of the two viruses may emerge, depending on the model parameters
Predicting wildlife reservoirs and global vulnerability to zoonotic Flaviviruses.
Flaviviruses continue to cause globally relevant epidemics and have emerged or re-emerged in regions that were previously unaffected. Factors determining emergence of flaviviruses and continuing circulation in sylvatic cycles are incompletely understood. Here we identify potential sylvatic reservoirs of flaviviruses and characterize the macro-ecological traits common to known wildlife hosts to predict the risk of sylvatic flavivirus transmission among wildlife and identify regions that could be vulnerable to outbreaks. We evaluate variability in wildlife hosts for zoonotic flaviviruses and find that flaviviruses group together in distinct clusters with similar hosts. Models incorporating ecological and climatic variables as well as life history traits shared by flaviviruses predict new host species with similar host characteristics. The combination of vector distribution data with models for flavivirus hosts allows for prediction of global vulnerability to flaviviruses and provides potential targets for disease surveillance in animals and humans
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