Dispersal, disease and life-history evolution

Castillo‐Chavez, Carlos; Yakubu, Abdul Aziz

doi:10.1016/s0025-5564(01)00065-7

Cited by 83 publications

(101 citation statements)

References 33 publications

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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%

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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%

“…The set of iterates of the p -periodic dynamical system { F 0, F 1, ..., F ( p 2 1)} is equivalent to the set of density sequences generated by model (2). In models (4) and (7),…”

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%

“…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%

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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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Reduction of discrete‐time infectious disease models

Parra

2023

Math Methods in App Sciences

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In this work, we propose the construction of discrete-time systems with two time scales in which infectious diseases dynamics are involved. We deal with two general situations. In the first, we consider that individuals affected by the disease move between generalized sites on a faster time scale than the dynamics of the disease itself. The second situation includes the dynamics of the disease acting faster together with another slower general process. Once the models have been built, conditions are established so that the analysis of the asymptotic behavior of their solutions can be carried out through reduced models. This is done using known reduction results for discrete-time systems with two time scales. These results are applied in the analysis of two new models. The first of them illustrates the first proposed situation, being the local dynamics of the SIS-type disease.Conditions are found for the eradication or global endemicity of the disease. In the second model, a case of co-infection with a primary disease and an opportunistic disease is treated, the latter acting faster than the former. Conditions for eradication and endemicity of co-infection are proposed.

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Dispersal, disease and life-history evolution

Cited by 83 publications

References 33 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

Reduction of discrete‐time infectious disease models

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