A geometric analysis of the SIRS epidemiological model on a homogeneous network

@article{JardonKojakhmetov2020AGA,
  title={A geometric analysis of the SIRS epidemiological model on a homogeneous network},
  author={Hildeberto Jard'on-Kojakhmetov and Christian Kuehn and Andrea Pugliese and Mattia Sensi},
  journal={Journal of Mathematical Biology},
  year={2020},
  volume={83}
}
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… 

A minimal model for adaptive SIS epidemics

The interplay between disease spreading and personal risk perception is of key importance for modelling the spread of infectious diseases. We propose a planar system of ordinary differential equations

Discrete epidemic models with two time scales

It is shown that there exist conditions under which a locally endemic disease, considering isolated patches in a metapopulation, can be eradicated globally by establishing the appropriate movements between patches.

The influence of a transport process on the epidemic threshold

A mean-field description of the stochastic network model is developed and it is shown that any transport process generally lowers the epidemic threshold because of the additional connections it generates, and also that random walks of fractional order are a more realistic model of human mobility.

A singularly perturbed vector-bias malaria model incorporating bed-net control

  • S. Salman
  • Mathematics
    Mathematical Methods in the Applied Sciences
  • 2022
A malaria transmission disease model with host selectivity and Insecticide treated bed nets (ITNs), as an intervention for controlling the disease, is formulated. Since the vector is an insect, the

Impact of Quarantine and Vaccination Policies on Viral Load

It is demonstrated that quarantine may play a crucial role in controlling an epidemic at its early stages, as well as the importance of early and widespread implementation of a vaccination program.

From subcritical behavior to a correlation-induced transition in rumor models

Rumors and information spreading emerge naturally from human-to-human interactions and have a growing impact on our everyday life due to increasing and faster access to information, whether

Entry-exit functions in fast-slow systems with intersecting eigenvalues

We study delayed loss of stability in a class of fast-slow systems with two fast variables and one slow one, where the linearisation of the fast vector field along a one-dimensional critical manifold

Applications of Machine Learning in Battling Against Novel COVID-19

This paper strongly analyze the Coronavirus Diseases (Covid-19) via utilizing the machine learning depended on classification as well as clustering method to overcome the challenge of new COVID-19 forecasting: the lack of historical data.

References

SHOWING 1-10 OF 51 REFERENCES

Dynamical analysis and perturbation solution of an SEIR epidemic model

Correlation models for childhood epidemics

Three pair models are introduced which attempt to capture the underlying heterogeneous structure of communicable disease by studying the connections and correlations between individuals, focusing on measles.

SIR dynamics in random networks with heterogeneous connectivity

  • E. Volz
  • Mathematics
    Journal of mathematical biology
  • 2008
The dynamic equations provide an alternative way of determining the epidemic threshold where large-scale epidemics are expected to occur, and below which epidemic behavior is limited to finite-sized outbreaks.

The saturating contact rate in marriage- and epidemic models

This note shows how to derive an expression for the saturating contact rate of individual contacts in a population that mixes randomly, by a mechanistic argument, and applies it to mathematical epidemiology and marriage models.

Thresholds for epidemic spreading in networks

It is conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.

Solvability of implicit final size equations for SIR epidemic models.

...