Extending the SIR epidemic model

Satsuma, Junkichi; Willox, Ralph; Ramani, A.; Grammaticos, B.; Cârstea, A. S.

doi:10.1016/j.physa.2003.12.035

Cited by 150 publications

(90 citation statements)

References 3 publications

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“…In [14], it is shown that the three models (3), (4), and (5) share the qualitative property that every solution converges to an equilibrium. Following [14,[17][18][19], let us derive (5) from (4). For > 0, we introduce a variable via = / (6) and parameters and > 0 through…”

Section: Differential and Difference Logistic Equationsmentioning

confidence: 99%

Convergence of a Logistic Type Ultradiscrete Model

Sekiguchi

Ishiwata²,

Nakata³

2017

Discrete Dynamics in Nature and Society

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We derive a piecewise linear difference equation from logistic equations with time delay by ultradiscretization. The logistic equation that we consider in this paper has been shown to be globally stable in the continuous and discrete time formulations. Here, we study if ultradiscretization preserves the global stability property, analyzing the asymptotic behaviour of the obtained piecewise linear difference equation. It is shown that our piecewise linear difference equation has a threshold property concerning global attractivity of equilibria, similar to the stable logistic equations with time delay.

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Section: Differential and Difference Logistic Equationsmentioning

confidence: 99%

Convergence of a Logistic Type Ultradiscrete Model

Sekiguchi

Ishiwata²,

Nakata³

2017

Discrete Dynamics in Nature and Society

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“…The susceptible-infective-recovered (SIR) model is first developed by Kermack and McKerdrick as a dynamic mathematical model and traditionally is used to estimate quantitatively population average parameters in epidemics [5]- [7]. In this paper, we attempts to apply SIR model to examine the socioeconomic, political, cultural conditions status as the parameters for observing population dynamics in an e-waste recycling system.…”

Section: Sir Modelmentioning

confidence: 99%

Understanding population dynamics of WEEE recycling system in the developing countries: A SIR model

Wu¹,

Chen²

2008

2008 IEEE International Symposium on Electronics and the Environment

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NTIL recently, literature indicates that it causes the growing concern over how the developing countries will manage largely volumes of e-waste (waste electrical and electronic equipment, WEEE) [1]- [4]. The reason is that e-waste disposal contains both highly valuable materials and toxic/hazardous substances, which may result in not only economical revenues but also negative impacts on human health and the environment when handling WEEE.Nowadays in South Africa, the formal sector, which is complying with international environmental standards, dominates handling WEEE industry. Whereas in some developing countries such as China, informal sector is the main WEEE processing system in which e-waste is treated by dangerous and inappropriate recycling practices [2], [4].Due to the nature of informal sector, the quality of informal processing activities and quantities of e-waste disposal are far than understood. Consequently, the existing situation of WEEE practices in the industrializing countries highlights the informal sector as a crucial and emerging issue, which is needed to be well understood and better governed.

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“…Some classical theory models for infectious disease emergencies include the Susceptible-InfectedRecovered (SIR) model, the Susceptible-Infected-Susceptible (SIS) model, and the SusceptibleExposed-Infected-Recovered (SEIR) model [4][5][6][7][8][9][10]. The mathematical simulation models based on these classical theory models primarily use logistics or differential equations to analyze the ratio changes in different time dimensions for individuals in each state (S, I, E, or R) [11,12].…”

Section: Introductionmentioning

confidence: 99%

SIS evolutionary game model and multi-agent simulation of an infectious disease emergency

Yang

Qing

Liu

et al. 2015

THC

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Abstract. BACKGROUND: Susceptible-Infected-Susceptible (SIS) infectious disease outbreaks are hazardous events. However, if governments sectors do not adequately supervise such outbreaks, these infectious diseases could spread significantly, resulting in large economic losses and social issues. OBJECTIVE: In this paper, an evolutionary game and simulation model based on the interactions between strategies and states was proposed, and the game between the public and government sectors and its impact on epidemic situations was discussed. METHODS: Replicator dynamics equations and the multi-agent model simulation were used for analysis. RESULTS: According to replicator dynamics equations as well as the multi-agent model simulation, the public all eventually adopted the mobility strategy. In addition, the supervision strength of the governmental sectors was equal to 0 after the strength fluctuated at a low level under the trigger strategy. Ultimately, the entire public shifted to the S state throughout the course of the emergency. CONCLUSIONS: Social order was maintained and social loss was controlled to a certain extent in the final analysis.

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Extending the SIR epidemic model

Cited by 150 publications

References 3 publications

Convergence of a Logistic Type Ultradiscrete Model

Convergence of a Logistic Type Ultradiscrete Model

Understanding population dynamics of WEEE recycling system in the developing countries: A SIR model

SIS evolutionary game model and multi-agent simulation of an infectious disease emergency

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