scholarly journals OPTIMAL LATENT PERIOD IN A BACTERIOPHAGE POPULATION MODEL STRUCTURED BY INFECTION-AGE

2011 ◽  
Vol 21 (04) ◽  
pp. 693-718 ◽  
Author(s):  
ÀNGEL CALSINA ◽  
JOSEP M. PALMADA ◽  
JORDI RIPOLL
Keyword(s):  
Latent Period ◽  
Evolutionarily Stable Strategy ◽  
Optimization Procedure ◽  
Infection Process ◽  
Death Process ◽  
Single Infection ◽  
Arbitrary Distribution ◽  
Infection Age ◽  
Population Dynamics Model ◽  
Age Structured

We study the lysis timing of a bacteriophage population by means of a continuously infection-age-structured population dynamics model. The features of the model are the infection process of bacteria, the death process, and the lysis process which means the replication of bacteriophage viruses inside bacteria and the destruction of them. The time till lysis (or latent period) is assumed to have an arbitrary distribution. We have carried out an optimization procedure, and we have found that the latent period corresponding to maximal fitness (i.e. maximal growth rate of the bacteriophage population) is of fixed length. We also study the dependence of the optimal latent period on the amount of susceptible bacteria and the number of virions released by a single infection. Finally, the evolutionarily stable strategy of the latent period is also determined as a fixed period taking into account that super-infections are not considered.

Management of evolving fish stocks

1998 ◽  
Vol 55 (8) ◽  
pp. 1971-1982 ◽  
Author(s):  
Mikko Heino
Keyword(s):  
Maximum Sustainable Yield ◽  
Evolutionary Change ◽  
Fish Stock ◽  
Sustainable Yield ◽  
Harvest Rate ◽  
Fish Stocks ◽  
Population Dynamics Model ◽  
Before And After ◽  
Age Structured ◽  
Delayed Maturation

Mortality caused by harvesting can select for life history changes in the harvested stock. Should this possibility be taken into account in the management of renewable resources? I compare the performance of different harvest strategies when evolutionary change is accounted for with the help of an age-structured population dynamics model. Assuming that age of first reproduction is the only evolving trait, harvesting of only mature individuals selects for delayed maturation and results in increased sustainable yields. Unselective harvesting of both mature and immature fish selects for earlier maturation which causes the sustainable yield to decrease. Constant stock size and constant harvest rate strategies perform equally well in terms of maximum sustainable yield, both before and after evolutionary change. The maximum sustainable yield for fixed-quota strategies is lower. All those strategies have similar evolutionary consequences given a similar average harvest rate. Coevolutionary dynamics between fish stock and the stock manager indicate that the evolutionary benefits of selective harvesting are attainable without incurring yield losses in the near future.

scholarly journals Human Mobility and Epidemic Evolution

2021 ◽  
Author(s):  
Fabio Vanni ◽  
David Lambert ◽  
Luigi Palatella ◽  
Paolo Grigolini
Keyword(s):  
Reproduction Number ◽  
Human Mobility ◽  
Theoretical Framework ◽  
Infection Age ◽  
Mobility Data ◽  
Risk Of Disease ◽  
Age Structured ◽  
Using Data ◽  
Age Structured Model ◽  
The Impact

Abstract The CoViD-19 pandemic ceased to be describable by a susceptible-infected-recovered (SIR) model when lockdowns were enforced. We introduce a theoretical framework to explain and predict changes in the reproduction number of SARS-CoV-2 (Sudden Acute Respiratory Syndrome Coronavirus 2) in terms of individual mobility and interpersonal proximity (alongside other epidemiological and environmental variables) during and after the lockdown period. We use an infection-age structured model described by a renewal equation. The model predicts the evolution of the reproduction number up to a week ahead of well-established estimates used in the literature. We show how lockdown policies, via reduction of proximity and mobility, reduce the impact of CoViD-19 and mitigate the risk of disease resurgence. We validate our theoretical framework using data from Google, Voxel51, Unacast, The CoViD-19 Mobility Data Network, and Analisi Distribuzione Aiuti.

scholarly journals On the use of aggregated human mobility data to estimate the reproduction number

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Fabio Vanni ◽  
David Lambert ◽  
Luigi Palatella ◽  
Paolo Grigolini
Keyword(s):  
Reproduction Number ◽  
Human Mobility ◽  
Theoretical Framework ◽  
Infection Age ◽  
Mobility Data ◽  
Risk Of Disease ◽  
Age Structured ◽  
Using Data ◽  
Age Structured Model ◽  
The Impact

AbstractThe reproduction number of an infectious disease, such as CoViD-19, can be described through a modified version of the susceptible-infected-recovered (SIR) model with time-dependent contact rate, where mobility data are used as proxy of average movement trends and interpersonal distances. We introduce a theoretical framework to explain and predict changes in the reproduction number of SARS-CoV-2 in terms of aggregated individual mobility and interpersonal proximity (alongside other epidemiological and environmental variables) during and after the lockdown period. We use an infection-age structured model described by a renewal equation. The model predicts the evolution of the reproduction number up to a week ahead of well-established estimates used in the literature. We show how lockdown policies, via reduction of proximity and mobility, reduce the impact of CoViD-19 and mitigate the risk of disease resurgence. We validate our theoretical framework using data from Google, Voxel51, Unacast, The CoViD-19 Mobility Data Network, and Analisi Distribuzione Aiuti.

scholarly journals sPop: Age-structured discrete-time population dynamics model in C, Python, and R

F1000Research ◽  
2020 ◽  
Vol 7 ◽  
pp. 1220
Author(s):  
Kamil Erguler
Keyword(s):  
Population Dynamics ◽  
Discrete Time ◽  
Uniform Design ◽  
Disease Spread ◽  
Dependent Manner ◽  
Dynamics Model ◽  
Fixed Rate ◽  
Animal Populations ◽  
Population Dynamics Model ◽  
Age Structured

This article describes the sPop packages implementing the deterministic and stochastic versions of an age-structured discrete-time population dynamics model. The packages enable mechanistic modelling of a population by monitoring the age and development stage of each individual. Survival and development are included as the main effectors and they progress at a user-defined pace: follow a fixed rate, delay for a given time, or progress at an age-dependent manner. The model is implemented in C, Python, and R with a uniform design to ease usage and facilitate adoption. Early versions of the model were previously employed for investigating climate-driven population dynamics of the tiger mosquito and the chikungunya disease spread by this vector. The sPop packages presented in this article enable the use of the model in a range of applications extending from vector-borne diseases towards any age-structured population including plant and animal populations, microbial dynamics, host-pathogen interactions, infectious diseases, and other time-dependent epidemiological processes.

scholarly journals sPop: Age-structured discrete-time population dynamics model in C, Python, and R

F1000Research ◽  
2018 ◽  
Vol 7 ◽  
pp. 1220 ◽  
Author(s):  
Kamil Erguler
Keyword(s):  
Population Dynamics ◽  
Discrete Time ◽  
Uniform Design ◽  
Disease Spread ◽  
Dependent Manner ◽  
Dynamics Model ◽  
Fixed Rate ◽  
Animal Populations ◽  
Population Dynamics Model ◽  
Age Structured

This article describes the sPop packages implementing the deterministic and stochastic versions of an age-structured discrete-time population dynamics model. The packages enable mechanistic modelling of a population by monitoring the age and development stage of each individual. Survival and development are included as the main effectors and they progress at a user-defined pace: follow a fixed-rate, delay for a given time, or progress at an age-dependent manner. The model is implemented in C, Python, and R with a uniform design to ease usage and facilitate adoption. Early versions of the model were previously employed for investigating climate-driven population dynamics of the tiger mosquito and the chikungunya disease spread by this vector. The sPop packages presented in this article enable the use of the model in a range of applications extending from vector-borne diseases towards any age-structured population including plant and animal populations, microbial dynamics, host-pathogen interactions, infectious diseases, and other time-delayed epidemiological processes.

The extinction time of a birth, death and catastrophe process and of a related diffusion model

1985 ◽  
Vol 17 (01) ◽  
pp. 42-52 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Population Size ◽  
Diffusion Processes ◽  
Death Process ◽  
Arbitrary Distribution ◽  
Initial Population ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Expected Time ◽  
Time To Extinction ◽  
Initial Population Size

The distribution of the extinction time for a linear birth and death process subject to catastrophes is determined. The catastrophes occur at a rate proportional to the population size and their magnitudes are random variables having an arbitrary distribution with generating function d(·). The asymptotic behaviour (for large initial population size) of the expected time to extinction is found under the assumption that d(.) has radius of convergence greater than 1. Corresponding results are derived for a related class of diffusion processes interrupted by catastrophes with sizes having an arbitrary distribution function.

Global dynamics in an age-structured HIV model with humoral immunity

2021 ◽  
pp. 2150047
Author(s):  
Zhongzhong Xie ◽  
Xiuxiang Liu
Keyword(s):  
Differential Equations ◽  
Humoral Immunity ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Hiv Model ◽  
Infection Age ◽  
Number Formula ◽  
Infected Cells ◽  
Age Structured ◽  
Disease Free

In this paper, we formulate an age-structured HIV model, in which the influence of humoral immunity and the infection age of the infected cells are considered. The model is governed by three ordinary differential equations and two first-ordered partial differential equations and admits three equilibria: disease-free, immune-inactivated and immune-activated equilibria. We introduce two important thresholds: the basic reproduction number [Formula: see text] and immune-activated reproduction number [Formula: see text] and further show the global stability of above three equilibria in terms of [Formula: see text] and [Formula: see text], respectively. The numerical simulations are presented to illustrate our results.

Sign in / Sign up

Export Citation Format

Share Document