Epidemic spread in populations at demographic equilibrium

Rı́os-Soto, Karen R.; Castillo-Chavez, Carlos; Neubert, Michael G.; Titi, Edriss S.; Yakubu, Abdul‐Aziz

doi:10.1090/conm/410/07733

Cited by 10 publications

(19 citation statements)

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“…where γ a = γ (1 − a) ∈ (0, 1) is the (constant) effective survival rate per generation, and f : R + → R + models the birth or recruitment process [20,21,[27][28][29][30][31][32]37,38]. The assumption about the timing of recruitment allows compression of the age-structure of the model so that one can work with a minimum number of equations.…”

Section: Exploited Fish Demographic Equationmentioning

confidence: 99%

“…That is, β models the impact of prevalence on φ. When infections are modeled as Poisson processes, then φ β I (t) [10][11][12][13]20,21,32,38]. The frequency dependent discrete-time model implicitly assumes three distinct temporal phases.…”

Section: Discrete-time Exploited Fish Sis Epidemic Modelmentioning

confidence: 99%

“…In continuous-time epidemic models, it is known that these assumptions are not universally applicable [1][2][3][4][5][6][10][11][12][13]20,21,32,38].…”

Section: Reproduction (Both S and I Reproduce Into S)mentioning

confidence: 99%

“…We compute 0 and used it to predict fish disease persistence or extinction when the exploited fish population dynamics are compensatory and the strong Allee effect is either present or absent and when the total population is growing at a geometric rate [4,5,[10][11][12][13]20,21,26,32,[35][36][37][38]. As in [10][11][12][13]38], when the stock demographic dynamics are overcompensatory, we numerically explore the relationship between the stock demographic equation and the epidemic process.…”

mentioning

confidence: 99%

“…When the stock recruitment function is a modified Beverton-Holt model, then the population has the strong Allee effect. However, when the stock recruitment function is the Ricker model [7,8,[16][17][18]20,21,[23][24][25][26][27][28][29][30][31][32][35][36][37][38][39], then the fish population dynamics are overcompensatory, and the stock demographic equation is capable of supporting complex dynamics such as period-doubling bifurcations route to chaos. In Sect.…”

mentioning

confidence: 99%

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Discrete-time exploited fish epidemic models

Yakubu

Ziyadi

2011

Afr. Mat.

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We extend classic discrete-time susceptible-infective-susceptible (SIS) and susceptible-exposed-infectious-susceptible epidemic models to include disease transmission dynamics in exploited fish populations that exhibit compensatory (contest competition) and overcompensatory (scramble competition) stock dynamics with and without the strong Allee effect. We compute the basic reproductive number, 0 , and use it to predict the (uniform) persistence or extinction of the infective exploited fish population, where the fish stock dynamics are compensatory and the strong Allee mechanism is either present or absent. We use the SIS epidemic model to explore the relationship between the stock demographic equation and the epidemic process, where the total stock population dynamics are overcompensatory. As in "higher" human and animal populations, we show that the demographic exploited fish population dynamics drive both the susceptible and infective stock dynamics.

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Section: Exploited Fish Demographic Equationmentioning

confidence: 99%

Section: Discrete-time Exploited Fish Sis Epidemic Modelmentioning

confidence: 99%

“…In continuous-time epidemic models, it is known that these assumptions are not universally applicable [1][2][3][4][5][6][10][11][12][13]20,21,32,38].…”

Section: Reproduction (Both S and I Reproduce Into S)mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Discrete-time exploited fish epidemic models

Yakubu

Ziyadi

2011

Afr. Mat.

Self Cite

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Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models

Franke

Yakubu

2008

J. Math. Biol.

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The dynamics of simple discrete-time epidemic models without disease-induced mortality are typically characterized by global transcritical bifurcation. We prove that in corresponding models with disease-induced mortality a tiny number of infectious individuals can drive an otherwise persistent population to extinction. Our model with disease-induced mortality supports multiple attractors. In addition, we use a Ricker recruitment function in an SIS model and obtained a three component discrete Hopf (Neimark-Sacker) cycle attractor coexisting with a fixed point attractor. The basin boundaries of the coexisting attractors are fractal in nature, and the example exhibits sensitive dependence of the long-term disease dynamics on initial conditions. Furthermore, we show that in contrast to corresponding models without disease-induced mortality, the disease-free state dynamics do not drive the disease dynamics.

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Models for the spread of white pine blister rust

Leung

Kot

2015

Journal of Theoretical Biology

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White pine blister rust (WPBR, Cronartium ribicola) is a fungal pathogen and a threat to whitebark pines (Pinus albicaulis). It has a complex life cycle that requires two hosts, a white pine and an alternate host, typically a currant or gooseberry (Ribes spp.). WPBR is transmitted between hosts by means of two types of airborne spores whose average dispersal distances differ by several orders of magnitude. In this paper, we introduce a discrete-time model based on the life cycle of WPBR. We then extend this model to include a continuous spatial domain, disease-induced mortality in the pines, and a latency period. After each extension, we find the pathogen's asymptotic speed of invasion analytically using exponential transforms and the method of steepest descent. Our results show that invasion speeds are strongly reduced by the latency period in the pine host. In addition, these speeds are highly dependent on the carrying capacity and infectiousness of each host type. If these parameters are sufficiently small, high mortality in pines may stop the spread of WPBR completely.

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Epidemic spread in populations at demographic equilibrium

Cited by 10 publications

References 0 publications

Discrete-time exploited fish epidemic models

Discrete-time exploited fish epidemic models

Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models

Models for the spread of white pine blister rust

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