Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

Mandal, Partha Sarathi; Banerjee, Malay

doi:10.1051/mmnp/20127308

Cited by 10 publications

(3 citation statements)

References 35 publications

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“…Via first Hopf bifurcation, the endemic steady state loses its stability and periodic solutions bifurcate at β β crit while via second Hopf bifurcation, periodic oscillation vanishes and the system regains its stability at β β crit . The case where the endemic steady state changes its behavior from unstable to stable with the increment in parameter value is named as backward Hopf bifurcation [73]. So, in this example, the occurrence of second Hopf bifurcation at β β crit is the case of backward Hopf bifurcation.…”

Section: Hopf-hopf Bifurcation and Stability Switchmentioning

confidence: 99%

Nonlinear dynamics of a SIRI model incorporating the impact of information and saturated treatment with optimal control

2022

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In this article, we propose and analyze an infectious disease model with reinfection and investigate disease dynamics by incorporating saturated treatment and information effect. In the model, we consider the case where an individual's immunity deteriorates and they become infected again after recovering. According to our findings, multiple steady states and backward bifurcation may occur as a result of treatment saturation. Further, if treatment is available for all, the disease will be eradicated provided R 0 < 1; however, because limited medical resources caused saturation in treatment, the disease may persist even if R 0 < 1. The global stability of the unique endemic steady state is established using a geometric approach. We also establish certain conditions on the transmission rate for the occurrence of periodic oscillations in the model system. Among nonlinear dynamics, we show supercritical Hopf bifurcation, bi-stability, backward Hopf bifurcation, and double Hopf bifurcation. To illustrate and validate our theoretical results, we present numerical examples. We found that when disease information coverage is high, infection cases fall considerably, and the disease persists when the reinfection rate is high. We then extend our model by incorporating two time-dependent controls, namely inhibitory interventions and treatment. Using Pontryagin's maximum principle, we prove the existence of optimal control paths and find the optimal pair of controls. According to our numerical simulations, the second control is less effective than the first. Furthermore, while implementing a single intervention at a time may be effective, combining both interventions is most effective in reducing disease burden and cost.

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Section: Hopf-hopf Bifurcation and Stability Switchmentioning

confidence: 99%

Nonlinear dynamics of a SIRI model incorporating the impact of information and saturated treatment with optimal control

2022

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“…Finally, we like to remark that the validation of our analytical findings for realistic ecosystem demand the appropriate estimation for the parameters and strengths of environmental forcing along with the choice of appropriate time scale. In near future we will also investigate the same model by taking care of demographic stochasticity [61] for parameter values within and outside the chaotic regime.…”

Section: Discussionmentioning

confidence: 99%

Multiplicative-noise Can Suppress Chaotic Oscillation in Lotka-Volterra Type Competitive Model

Mandal

Banerjee

2012

Math. Model. Nat. Phenom.

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Abstract. Recently, Wang and Xiao studied a four-dimensional competitive Lotka-Volterra system within a deterministic environment in [11]. With the help of numerical example they showed the existence of a chaotic attractor through the period doubling route. In this paper, we are interested to study the dynamics of the same model in presence of environmental driving forces. To incorporate the environmental driving force into the deterministic system, we perturb the growth rates of each species by white noise terms. Then we prove that the unique positive global solution exists for the noise added system and the general p-th order moment of it is bounded for p ≥ 1, which ensures that the solution is stochastically bounded. It is also shown that the solution of the stochastic system is stochastically permanent under some simple conditions. Finally , we demonstrate the noise induced oscillation for the concerned model with the help of numerical example..

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“…During the past few decades, various scientific approaches and mathematical methods were developed and applied to model the dynamics of the spread of infectious diseases [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. Numerous studies have also examined the dynamics of SARS [ 21 , 22 , 23 , 24 ] and COVID-19 [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 ].…”

Section: Introductionmentioning

confidence: 99%

Complexity of COVID-19 Dynamics

Sivakumar

Deepthi

2021

Entropy

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With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made to understand the spread of COVID-19, our knowledge of the COVID-19 dynamics still remains limited. The present study employs the concepts of chaos theory to examine the temporal dynamic complexity of COVID-19 around the world. The false nearest neighbor (FNN) method is applied to determine the dimensionality and, hence, the complexity of the COVID-19 dynamics. The methodology involves: (1) reconstruction of a single-variable COVID-19 time series in a multi-dimensional phase space to represent the underlying dynamics; and (2) identification of “false” neighbors in the reconstructed phase space and estimation of the dimension of the COVID-19 series. For implementation, COVID-19 data from 40 countries/regions around the world are studied. Two types of COVID-19 data are analyzed: (1) daily COVID-19 cases; and (2) daily COVID-19 deaths. The results for the 40 countries/regions indicate that: (1) the dynamics of COVID-19 cases exhibit low- to medium-level complexity, with dimensionality in the range 3 to 7; and (2) the dynamics of COVID-19 deaths exhibit complexity anywhere from low to high, with dimensionality ranging from 3 to 13. The results also suggest that the complexity of the dynamics of COVID-19 deaths is greater than or at least equal to that of the dynamics of COVID-19 cases for most (three-fourths) of the countries/regions. These results have important implications for modeling and predicting the spread of COVID-19 (and other infectious diseases), especially in the identification of the appropriate complexity of models.

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Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

Cited by 10 publications

References 35 publications

Nonlinear dynamics of a SIRI model incorporating the impact of information and saturated treatment with optimal control

Nonlinear dynamics of a SIRI model incorporating the impact of information and saturated treatment with optimal control

Multiplicative-noise Can Suppress Chaotic Oscillation in Lotka-Volterra Type Competitive Model

Complexity of COVID-19 Dynamics

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