Hopf bifurcation of an infection-age structured eco-epidemiological model with saturation incidence

2019 ◽  
Vol 477 (1) ◽  
pp. 398-419 ◽  
Author(s):  
Peng Yang ◽  
Yuanshi Wang
Keyword(s):  
Hopf Bifurcation ◽  
Epidemiological Model ◽  
Infection Age ◽  
Age Structured

Periodic Solutions of a Delayed Eco-Epidemiological Model with Infection-Age Structure and Holling Type II Functional Response

2020 ◽  
Vol 30 (01) ◽  
pp. 2050011 ◽  
Author(s):  
Peng Yang ◽  
Yuanshi Wang
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Age Structure ◽  
Epidemiological Model ◽  
Type Ii ◽  
Epidemic Disease ◽  
Semilinear Equations ◽  
Infection Age ◽  
Coexistence Equilibrium ◽  
Type Ii Functional Response

This paper is devoted to the study of a new delayed eco-epidemiological model with infection-age structure and Holling type II functional response. Firstly, the disease transmission rate function among the predator population is treated as the piecewise function concerning the incubation period [Formula: see text] of the epidemic disease and the model is rewritten as an abstract nondensely defined Cauchy problem. Besides, the prerequisite which guarantees the presence of the coexistence equilibrium is achieved. Secondly, via utilizing the theory of integrated semigroup and the Hopf bifurcation theorem for semilinear equations with nondense domain, it is found that the model exhibits a Hopf bifurcation near the coexistence equilibrium, which suggests that this model has a nontrivial periodic solution that bifurcates from the coexistence equilibrium as the bifurcation parameter [Formula: see text] crosses the bifurcation critical value [Formula: see text]. That is, there is a continuous periodic oscillation phenomenon. Finally, some numerical simulations are shown to support and extend the analytical results and visualize the interesting phenomenon.

scholarly journals Bifurcation Analysis of an Age Structured HIV Infection Model with Both Virus-to-Cell and Cell-to-Cell Transmissions

2018 ◽  
Vol 28 (09) ◽  
pp. 1850109 ◽  
Author(s):  
Xiangming Zhang ◽  
Zhihua Liu
Keyword(s):  
T Cells ◽  
Hopf Bifurcation ◽  
Hiv Infection ◽  
Bifurcation Analysis ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Positive Equilibrium ◽  
Semilinear Equations ◽  
Age Structured ◽  
Hiv Infection Model

We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of uninfected CD[Formula: see text] T cells by a logistic function and the infected CD[Formula: see text] T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some parameter values such that this HIV infection model has a nontrivial periodic solution which bifurcates from the positive equilibrium. The numerical simulations are also carried out.

scholarly journals Epidemiological model of COVID-19 in healthcare workers: occupational vs. environmental disease

2021 ◽  
Vol 72 (1) ◽  
pp. 6-11
Author(s):  
Mihaela Stoia
Keyword(s):  
Occupational Exposure ◽  
Healthcare Workers ◽  
Strong Predictor ◽  
Epidemiological Model ◽  
Healthcare Sector ◽  
Healthcare Personnel ◽  
Nursing Assistant ◽  
Term Care ◽  
Frontline Staff ◽  
Infection Age

Abstract This study aims to estimate the occupational etiology of COVID-19 in the healthcare sector and obtain a risk matrix for the burden of disease across occupations and specific activities. The study population included 4515 cases and 133077 controls. We have used an epidemiological model that included data collected over one year from employed persons with confirmed SARS-CoV-2 infection, age group 20-64, and residing in Sibiu County. We measured the incidence rate (IR), relative risk (RR), and risk of COVID-19 attributable to the occupational exposure (AR), respectively, statistical analysis based on frequency distribution and the portion of cases to compute the risk levels in social- and healthcare workers. According to this model, approximately 70.5% of COVID-19 risk could be attributable to occupational exposure. The workplace is a strong predictor of infection risk (RR 3.4), particularly in residential long-term care facilities, hospitals, and ambulance services. The highest-risk job functions are nurse, nursing assistant, ambulance worker, and dentist. In conclusion, we believe in having demonstrated that epidemiological modeling may be helpful for risk management and notification of COVID-19 as an occupational disease in frontline staff and essential healthcare personnel.

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.

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