Discrete-time S-I-S models with complex dynamics

Castillo‐Chavez, Carlos; Yakubu, Abdul‐Aziz

doi:10.1016/s0362-546x(01)00587-9

Cited by 95 publications

(87 citation statements)

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“…R þ models the birth or recruitment process [2,3]. In periodic environments, either the recruitment function or the survivalr ate is p -periodically forced.…”

Section: Periodically Forced Demographic Equationsmentioning

confidence: 99%

Population models with periodic recruitment functions and survival rates

Franke

Yakubu

2005

Journal of Difference Equations and Applications

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We study the combined effects of periodically varying carrying capacity and survivalrate on populations. We showthat our populations with constant recruitment functions do not experience either resonance or attenuance when either only the carrying capacity or the survivalrate is fluctuating. However,when both carrying capacity and survivalr ate are fluctuatingt he populations experience either attenuance or resonance, depending on parameter regimes. In addition, we showthat our populations with BevertonHolt recruitment functions experience attenuance when only the carrying capacity is fluctuating.

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“…R þ models the birth or recruitment process [2,3]. In periodic environments, either the recruitment function or the survivalr ate is p -periodically forced.…”

Section: Periodically Forced Demographic Equationsmentioning

confidence: 99%

Population models with periodic recruitment functions and survival rates

Franke

Yakubu

2005

Journal of Difference Equations and Applications

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“…length of the infectious period in generations; "( is the proportion of surviving susceptibles who can be invaded by the disease; and, -aG' (0) is the maximum rate of infection per infective [9,10]. Since ( 1 --y)(~r\)+(I--yu) gives the demographic death-adjusted infectious period measured in generations then ~ decreases with population growth (~d > 1) and increases with population decay (0 < ~d < 1), that is, whenever ~d =J 1 demography has an impact.…”

Section: I+jl I+jlmentioning

confidence: 99%

“…and nd = ~· Using proportions reduces System (10) to the following system of equations (see, [6,9,10]):…”

Section: {B) If ~0 > 1 Then All Solutions (S(n)i(n)) Approach a Unimentioning

confidence: 99%

“…Simple nonlinear disnete-time population models are capable of generating complex (chaotic) dynamics [4,6,9,18,21,22]. A simple nonlinear discretetime susceptible-infeded-susceptible (S-I-S) epidemic model that assumes that the population is either asymptotically bounded, experiences geometric growth or is capable of generating complex dynamics is presented.…”

Section: Introductionmentioning

confidence: 99%

“…Barrera et al [6]; Velazquez [27]; and Castilla-Chavez and Yakubu [9,10] have developed models for the study of disease dynamics in populations with discrete generations and potentially complex (chaotic) disease-free dynamics. The models in this article overlap somewhat with (S-I-S) epidemic models found in the literature (see [6,9,10,16,27]). …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Discrete-Time S-I-S Models With Simple and Complex Population Dynamics

Castillo‐Chavez¹,

Yakabu²

2002

Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction

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The model for this study is an extension of a nonlinear discrete-time susceptibleinfected-susceptible (S-1-S) epidemic model of Barrera et al. and Velazquez that includes populations exhibiting geometric, bounded or complex dynamics. Thresholds for disease persistence are computed and used to illustrate the analysis of the asymptotic global behavior of solutions. Extensions and results that include SIS models capable of supporting multiple attractors are discussed .· Extensions and results that include SIS models capable of supporting multiple attractors are discussed. DISCRETE-TIME S-I-S MODELS WITH SIMPLE AND COMPLEX POPULATION DYNAMICS

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Various epidemic models on complex networks

Small

Chen

2014

Propagation Dynamics on Complex Networks

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Discrete-time S-I-S models with complex dynamics

Cited by 95 publications

References 0 publications

Population models with periodic recruitment functions and survival rates

Population models with periodic recruitment functions and survival rates

Discrete-Time S-I-S Models With Simple and Complex Population Dynamics

Various epidemic models on complex networks

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