Threshold Dynamics and Stability of Epidemic Models with Periodically Varying Contact Rates
Author(s): Neeraj Kumar
Publication #: 2609037
Date of Publication: 08.12.2016
Country: India
Pages: 1-17
Published In: Volume 2 Issue 6 December-2016
DOI: https://doi.org/10.62970/IJIRCT.v2.i6.2609037
Abstract
The fluctuations in human contact patterns can become a significant factor in the transmission and persistence of infectious diseases. In this work, we have developed a nonlinear SEIQR epidemic model to study the dynamics of epidemic with periodically varying contact rates. We break down the population into susceptible, exposed, infectious, quarantined, and recovered bodies and we consider demographic turnover, disease-causing mortality, disease progression from exposure to infection, and isolation of the infectious population. The contact rate is assumed to vary in time, and this model can be used to explain seasonal changes in population interaction. We have established the properties of the model, such as positivity and boundedness of solutions. A threshold quantity for disease invasions and extinction is derived from the linearized infection subsystem, and the stability of the disease-free state in the periodic setting is investigated. The impact of periodic forcing, isolation, progression, and recovery parameters on the persistence of the epidemic is investigated. We conduct numerical simulations to illustrate some of our analytical results and to show how changes in the amplitude and frequency of contact-rate fluctuations have the effect of time-dependent changes in the persistence of infection. Our findings give us a mathematical framework for how the periodic change in contact patterns and intervention through isolation can affect the persistence of the epidemic and its stability to a certain extent.
Keywords: SEIQR epidemic model; Periodic contact rate; Threshold dynamics; Stability analysis; Periodic forcing; Disease persistence; Quarantine; Epidemic modeling; Mathematical epidemiology; Floquet theory.
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