Paradoxical phenomena and chaotic dynamics in epidemic models subject to vaccination

Abstract

An alternative to the constant vaccination strategy could be the administration of a large number of doses on "immunization days" with the aim of maintaining the basic reproduction number to be below one. This strategy, known as pulse vaccination, has been successfully applied for the control of many diseases especially in low-income countries. In this paper, we analytically prove (without being computer-aided) the existence of chaotic dynamics in the classical SIR model with pulse vaccination. To the best of our knowledge, this is the first time in which a theoretical proof of chaotic dynamics is given for an epidemic model subject to pulse vaccination. In a realistic public health context, our analysis suggests that the combination of an insufficient vaccination coverage and high birth rates could produce chaotic dynamics and an increment of the number of infectious individuals.

The Role of Movement Patterns in Epidemic Models on Complex Networks

“…On the other hand, we always assume that the dynamical behavior of ( 1) is simple, namely the global attraction to an equilibrium. However, the presence of oscillations and chaotic patterns is broadly documented in epidemiology (Barrientos et al 2017;Ruiz-Herrera 2020). In this context, our results are not valid and a different approach is needed.…”

“…However, the presence of oscillations and chaotic patterns is broadly documented in epidemiology (Barrientos et al. 2017 ; Ruiz-Herrera 2020 ). In this context, our results are not valid and a different approach is needed.…”

FPGA Realizations of Chaotic Epidemic and Disease Models Including Covid-19

“…Susceptible, infected, recovered and possibly also exposed classes of a given population need to be considered. Many models have been developed for viral infectious diseases such as Influenza and Ebola [9]- [14] and nearly all of them show chaotic dynamics even after vaccination is administrated [15]. The emergence of chaotic behavior can be attributed mostly to predator-prey and competition dynamics [16]- [18] as well as nonlinear interactions between cell populations such as in cancer models [19]- [22] and Parkinson's disease [23], [24].…”