Global stability of an infection-age structured HIV-1 model linking within-host and between-host dynamics

2015 ◽  
Vol 263 ◽  
pp. 37-50 ◽  
Author(s):  
Mingwang Shen ◽  
Yanni Xiao ◽  
Libin Rong
Keyword(s):  
Global Stability ◽  
Infection Age ◽  
Age Structured ◽  
Hiv 1

scholarly journals Global stability in a competitive infection-age structured model

2020 ◽  
Vol 15 ◽  
pp. 54
Author(s):  
Quentin Richard
Keyword(s):  
Global Stability ◽  
Basin Of Attraction ◽  
Exclusion Principle ◽  
Globally Asymptotically Stable ◽  
Infection Age ◽  
Age Structured ◽  
The Stability ◽  
Globally Attractive ◽  
Age Structured Model ◽  
Disease Free

We study a competitive infection-age structured SI model between two diseases. The well-posedness of the system is handled by using integrated semigroups theory, while the existence and the stability of disease-free or endemic equilibria are ensured, depending on the basic reproduction number R0x and R0y of each strain. We then exhibit Lyapunov functionals to analyse the global stability and we prove that the disease-free equilibrium is globally asymptotically stable whenever max{R0x, R0y} ≤ 1. With respect to explicit basin of attraction, the competitive exclusion principle occurs in the case where R0x ≠ R0y and max{R0x, R0y} > 1, meaning that the strain with the largest R0 persists and eliminates the other strain. In the limit case R0x = Ry0 > 1, an infinite number of endemic equilibria exists and constitute a globally attractive set.

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.

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 Global stability of an age-structured cholera model

2014 ◽  
Vol 11 (3) ◽  
pp. 641-665 ◽  
Author(s):  
Jianxin Yang ◽  
◽  
Zhipeng Qiu ◽  
Xue-Zhi Li ◽  
Keyword(s):  
Global Stability ◽  
Age Structured
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