Intraspecific Competition, Dispersal and Disease Dynamics in Discrete-Time Patchy Environments

Castillo‐Chavez, Carlos; Yakubu, Abdul‐Aziz

doi:10.1007/978-1-4757-3667-0_10

Cited by 19 publications

(57 citation statements)

References 17 publications

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“…In constant environments, theoretical discrete-time epidemic models are usually formulated under the assumption that the dynamics of the total population size in generation t, denoted by N (t), is governed by equations of the form N (t + 1) = f (N (t)) + γN (t), (1) where γ ∈ (0, 1) is the constant "probability" of surviving per generation and f : R + → R + models the birth or recruitment process [7,9].…”

Section: Demographic Equations With Seasonalitymentioning

confidence: 99%

“…To understand the impact of seasonality and disease on life-history outcomes, we study the long-term dynamics of our model under specific functional forms for the periodic recruitment function. The periodic , the periodic constant, and the periodic Malthus (geometric growth) models are the periodic recruitment functions for this study [7,8,9].We assume that a disease invades and subdivides the target population into two classes: susceptibles (noninfectives) and infectives. Prior to the time of disease invasion, the population is assumed to be governed by a periodically forced demographic equation with a periodic recruitment function.…”

mentioning

confidence: 99%

“…The model reduces to the SIS epidemic model of Castillo-Chavez and Yakubu when the environment is constant (nonperiodic) [7,8,9]. To understand the impact of seasonality and disease on life-history outcomes, we study the long-term dynamics of our model under specific functional forms for the periodic recruitment function.…”

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confidence: 99%

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confidence: 99%

“…We also explore the relationship between the demographic equation and the epidemic process. Castillo-Chavez and Yakubu, in [7,8,9], show that in constant environments the demographic equation drives the disease dynamics. In stark contrast, we use numerical simulations to show that in periodic environments the demographic equation does not always drive the disease dynamics.…”

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confidence: 99%

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Discrete-Time SIS EpidemicModel in a Seasonal Environment

Yakubu¹,

Franke²

2006

SIAM J. Appl. Math.

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Abstract. We study the combined effects of seasonal trends and diseases on the extinction and persistence of discretely reproducing populations. We introduce the epidemic threshold parameter, R 0 , for predicting disease dynamics in periodic environments. Typically, in periodic environments, R 0 > 1 implies disease persistence on a cyclic attractor, while R 0 < 1 implies disease extinction. We also explore the relationship between the demographic equation and the epidemic process. In particular, we show that in periodic environments, it is possible for the infective population to be on a chaotic attractor while the demographic dynamics is nonchaotic. 1. Introduction. The complexities of a periodic environment can significantly affect the regulation of species [26]. In periodic environments, population sizes are often either enhanced via resonance or diminished via attenuance [5,10,11,13,14,15,16,17,18,19,20,23,24,25,30,31,32,33,34,35,37,38,45,48,50] [37,38], and others have studied the effects of periodic environments on ecological models without explicit disease dynamics [46].In this paper, we focus on the impact of seasonal factors on a discrete-time SIS (susceptible-infected-susceptible) epidemic model. The model reduces to the SIS epidemic model of Castillo-Chavez and Yakubu when the environment is constant (nonperiodic) [7,8,9]. To understand the impact of seasonality and disease on life-history outcomes, we study the long-term dynamics of our model under specific functional forms for the periodic recruitment function. The periodic , the periodic constant, and the periodic Malthus (geometric growth) models are the periodic recruitment functions for this study [7,8,9].We assume that a disease invades and subdivides the target population into two classes: susceptibles (noninfectives) and infectives. Prior to the time of disease invasion, the population is assumed to be governed by a periodically forced demographic equation with a periodic recruitment function. Hence, the population is assumed to be either at a demographic "steady state" (an attracting cycle) or growing at a periodic

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Section: Demographic Equations With Seasonalitymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Discrete-Time SIS EpidemicModel in a Seasonal Environment

Yakubu¹,

Franke²

2006

SIAM J. Appl. Math.

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The impact of constant effort harvesting on the dynamics of a discrete‐time contest competition model

AlSharawi

Amleh

2017

Math Methods in App Sciences

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In this paper, we study a general discrete-time model representing the dynamics of a contest competition species with constant effort exploitation. In particular, we consider the difference equationthe density dependent function f satisfies certain conditions that are typical of a contest competition. The harvesting parameter h is considered as the main parameter, and its effect on the general dynamics of the model is investigated. In the absence of delay in the recruitment (k = 0), we show the effect of h on the stability, the maximum sustainable yield, the persistence of solutions, and how the intraspecific competition change from contest to scramble competition. When the delay in recruitment is 1 (k = 1), we show that a Neimark-Sacker bifurcation occurs, and the obtained invariant curve is supercritical. Furthermore, we give a characterization of the persistent set.

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