Analysis of an SIRS epidemic model with time delay on heterogeneous network

Liu, Qiming; Sun, Meici; Li, Tao

doi:10.1186/s13662-017-1367-z

Cited by 12 publications

(10 citation statements)

References 21 publications

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“…Now, let us denote by g(t) the solution of the system , with Equations 16,(17), (18), where g ∶ R → R 3N and consider the case where…”

Section: Prop 33)mentioning

confidence: 99%

“…Moreover, we adopt an individual (node)-based approach, see also other studies 9,14 for SIRS-type node-based models. As opposite, a large part of the literature consider models in which the structure of the network is simplified by using a degree-based mean-field (DBMF) approach, [15][16][17][18] where all nodes with the same degree are assumed to be statistically equivalent. Thus, these kinds of models only reflect the evolution in time of the fraction of nodes with a certain degree k in each compartment, while neglecting the states of each single individual.…”

Section: Introductionmentioning

confidence: 99%

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Some aspects of the Markovian SIRS epidemic on networks and its mean‐field approximation

Ottaviano

Bonaccorsi

2020

Math Methods in App Sciences

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We study the spread of an SIRS‐type epidemic with vaccination on network. Starting from an exact Markov description of the model, we investigate the mean epidemic lifetime by providing a sufficient condition for fast extinction that depends on the model parameters and the topology of the network. Then, we pass to consider a first‐order mean‐field approximation of the exact model and its stability properties, by relying on the graph‐theoretical notion of equitable partition. In the case of graphs possessing this kind of partition, we prove that the endemic equilibrium can be computed by using a lower‐dimensional dynamical system. Finally, in the special case of regular graphs, we investigate the domain of attraction of the endemic equilibrium.

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“…Now, let us denote by g(t) the solution of the system , with Equations 16,(17), (18), where g ∶ R → R 3N and consider the case where…”

Section: Prop 33)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some aspects of the Markovian SIRS epidemic on networks and its mean‐field approximation

Ottaviano

Bonaccorsi

2020

Math Methods in App Sciences

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show abstract

“…In addition to computer virus models with time delay, there are also some other dynamical models with time delay, which have shown that time delay causes problems such as instability and restrict the conceivable performance of the control systems. For example, the predator-prey model [27][28][29][30], the epidemic model [31][32][33][34][35], and the neural network model [36][37][38][39]. All the mentioned works about delayed dynamical models have shown that time delay can produce complicated nonlinear phenomena with the change of time.…”

Section: Introductionmentioning

confidence: 99%

A delayed e-epidemic SLBS model for computer virus

2019

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We propose an e-epidemic time-delay Susceptible-Latent-Breaking out-Susceptible (SLBS) model to study delay dynamics appearing due to antivirus software, which takes time to clean the viruses from latent and breaking-out computers. We perform nonlinear stability analysis, Hopf bifurcation analysis, and its direction and stability. Numerical simulation results (time series analysis and bifurcation diagram) give useful insights for delay dynamics. We investigate the effect of the control parameters like rate of infection of all the classes and cure rates on the model system. Our results suggest that time delay is responsible for destabilizing the system dynamics. For smooth functionality of a computer system, our results suggest the minimum use of removable storage devices like smart phones, optical discs, memory cards, external hard disk, digital cameras, and so on and use of effective antivirus softwares.

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“…Overall, the model we consider can be classified as a SIRS susceptible-infectedremoved-susceptible model with vaccination, on networks, that we shall refer to with SIRS v . Moreover, we adopt an individual (node)-based approach , see also [35], as opposite to a large part of the literature where the structure of the network is simplified by using a degree-based mean-field (DBMF) approach, where all nodes with the same degree are assumed to be statistically equivalent, see, e.g., [11,22,23,37].…”

Section: Introductionmentioning

confidence: 99%

Some aspects of the Markovian SIRS epidemic on networks and its mean-field approximation

Ottaviano,

Bonaccorsi

2019

Preprint

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We study the spread of an SIRS-type epidemics with vaccination on network. Starting from an exact Markov description of the model we investigate the mean epidemic lifetime by providing a sufficient condition for the fast extinction, depending on the topology of the network.Then, we pass to consider a first-order mean-field approximation of the exact model. At this point, we dwell on the stability properties of the system by relying on the graph-theoretical notion of equitable partition. In the case of graphs possessing this kind of partition, we find a positively invariant set which contain the endemic equilibrium, that can be computed by using a lower-dimensional dynamical system. Finally, in the special case of regular graphs, we show that when the recovery rate is higher than the vaccination rate, the aforementioned invariant set is contained in the domain of attraction of the endemic equilibrium.

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Analysis of an SIRS epidemic model with time delay on heterogeneous network

Cited by 12 publications

References 21 publications

Some aspects of the Markovian SIRS epidemic on networks and its mean‐field approximation

Some aspects of the Markovian SIRS epidemic on networks and its mean‐field approximation

A delayed e-epidemic SLBS model for computer virus

Some aspects of the Markovian SIRS epidemic on networks and its mean-field approximation

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