scholarly journals Assessing the Impact of Prophylactic Vaccines on HPV Prevalence

2019 ◽  
Vol 20 (2) ◽  
pp. 305
Author(s):  
F. Azevedo ◽  
L. Esteva ◽  
Claudia P. Ferreira
Keyword(s):  
Vaccine Coverage ◽  
Transmission Rate ◽  
Geometric Mean ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Health Politics ◽  
Vaccination Strategies ◽  
The Impact

A mathematical model considering female and male individuals is proposed to evaluate vaccination strategies applied to control of HPV transmission in human population. The basic reproductive number of the disease, $R_0$, is given by the geometric mean of the basic reproductive number of female and male populations. The model has a globally asymptotically stable disease-free equilibrium whenever $R_0 <1$. Furthermore, it has an unique endemic state when $R_0$ exceeds unity which is globally asymptotically stable. Numerical simulations were done to compare several different vaccination schedules. The results showed that the vaccination strategies that do not include vaccination of men can only control the disease if more than 90\% of women are vaccinated. The sensitivity analysis indicated that the relevant parameters to control HPV transmission, in order of importance, are vaccine efficacy times the fraction of population that is vaccinated, disease recovery-rate, and disease transmission rate. Therefore, health politics that promoting the increase of vaccine coverage, and screening for the disease in both population can improve disease control.

Global properties for an age-structured within-host model with Crowley–Martin functional response

2017 ◽  
Vol 10 (02) ◽  
pp. 1750030 ◽  
Author(s):  
Shaoli Wang ◽  
Xinyu Song
Keyword(s):  
Functional Response ◽  
Viral Infections ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Multi Scale ◽  
Global Properties ◽  
Age Structured

Based on a multi-scale view, in this paper, we study an age-structured within-host model with Crowley–Martin functional response for the control of viral infections. By means of semigroup and Lyapunov function, the global asymptotical property of infected steady state of the model is obtained. The results show that when the basic reproductive number falls below unity, the infection dies out. However, when the basic reproductive number exceeds unity, there exists a unique positive equilibrium which is globally asymptotically stable. This model can be deduced to different viral models with or without time delay.

scholarly journals Global Stability of an SEIS Epidemic Model with General Saturation Incidence

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hui Zhang ◽  
Li Yingqi ◽  
Wenxiong Xu
Keyword(s):  
Latent Period ◽  
Epidemic Model ◽  
Convergence Theorem ◽  
Incidence Rates ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

We present an SEIS epidemic model with infective force in both latent period and infected period, which has different general saturation incidence rates. It is shown that the global dynamics are completely determined by the basic reproductive number R0. If R0≤1, the disease-free equilibrium is globally asymptotically stable in T by LaSalle’s Invariance Principle, and the disease dies out. Moreover, using the method of autonomous convergence theorem, we obtain that the unique epidemic equilibrium is globally asymptotically stable in T0, and the disease spreads to be endemic.

scholarly journals Global Dynamics of an HTLV-1 Model with Cell-to-Cell Infection and Mitosis

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Sumei Li ◽  
Yicang Zhou
Keyword(s):  
Chronic Infection ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Cell Infection ◽  
Globally Asymptotically Stable ◽  
Human T Cell

A mathematical model of human T-cell lymphotropic virus type 1 in vivo with cell-to-cell infection and mitosis is formulated and studied. The basic reproductive numberR0is derived. It is proved that the dynamics of the model can be determined completely by the magnitude ofR0. The infection-free equilibrium is globally asymptotically stable (unstable) ifR0<1  (R0>1). There exists a chronic infection equilibrium and it is globally asymptotically stable ifR0>1.

The impact of media coverage with a piecewise transmission rate in the spread of diseases

2016 ◽  
Vol 10 (01) ◽  
pp. 1750003
Author(s):  
Maoxing Liu ◽  
Lixia Zuo
Keyword(s):  
Basic Reproduction Number ◽  
Media Coverage ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Three Dimensional ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Contact Transmission ◽  
The Impact ◽  
The Basic Reproduction Number

A three-dimensional compartmental model with media coverage is proposed to describe the real characteristics of its impact in the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that media coverage exhibits its effect only when the number of the infected exceeds a certain critical level. Further, it is assumed that the impact of media coverage on the contact transmission is described by an exponential decreasing factor. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity and media coverage impact is sufficiently small, a unique endemic equilibrium exists, which is globally asymptotically stable.

SVIR epidemic model with age structure in susceptibility, vaccination effects and relapse

2017 ◽  
Vol 82 (5) ◽  
pp. 945-970 ◽  
Author(s):  
Jinliang Wang ◽  
Min Guo ◽  
Shengqiang Liu
Keyword(s):  
Age Structure ◽  
Epidemic Model ◽  
Lyapunov Functional ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Combined Effects ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Disease Free

Abstract An SVIR epidemic model with continuous age structure in the susceptibility, vaccination effects and relapse is proposed. The asymptotic smoothness, existence of a global attractor, the stability of equilibria and persistence are addressed. It is shown that if the basic reproductive number $\Re_0&lt;1$, then the disease-free equilibrium is globally asymptotically stable. If $\Re_0&gt;1$, the disease is uniformly persistent, and a Lyapunov functional is used to show that the unique endemic equilibrium is globally asymptotically stable. Combined effects of susceptibility age, vaccination age and relapse age on the basic reproductive number are discussed.

scholarly journals Dynamical Behavior of a New Epidemiological Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zizi Wang ◽  
Zhiming Guo
Keyword(s):  
Time Delay ◽  
Dynamical Behavior ◽  
Endemic Equilibrium ◽  
Epidemiological Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain timeτ. The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive numberR0is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease-free equilibrium is globally asymptotically stable provided thatR0≤1; ifR0>1, then there exists a unique endemic equilibrium, and it is globally asymptotically stable. For the model with time delay, a sufficient condition is given to ensure that the disease-free equilibrium is locally asymptotically stable. Hopf bifurcation in endemic equilibrium with respect to the timeτis also addressed.

Analysis of a sex-structured HIV/AIDS model with the effect of screening of infectives

2014 ◽  
Vol 07 (05) ◽  
pp. 1450054 ◽  
Author(s):  
S. Athithan ◽  
Mini Ghosh
Keyword(s):  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Epidemic Threshold ◽  
Heterosexual Contact ◽  
Globally Asymptotically Stable ◽  
Transmission Of Disease ◽  
Globally Stable ◽  
Disease Free ◽  
Hiv Aids

This paper presents a nonlinear sex-structured mathematical model to study the spread of HIV/AIDS by considering transmission of disease by heterosexual contact. The epidemic threshold and equilibria for the model are determined, local stability and global stability of both the "Disease-Free Equilibrium" (DFE) and "Endemic Equilibrium" (EE) are discussed in detail. The DFE is shown to be locally and globally stable when the basic reproductive number ℛ0 is less than unity. We also prove that the EE is locally and globally asymptotically stable under some conditions. Finally, numerical simulations are reported to support the analytical findings.

Dynamical analysis for delayed virus infection models with cell-to-cell transmission and density-dependent diffusion

2020 ◽  
Vol 13 (07) ◽  
pp. 2050060
Author(s):  
Shaoli Wang ◽  
Achun Zhang ◽  
Fei Xu
Keyword(s):  
Neumann Boundary ◽  
Basic Reproductive Number ◽  
Dynamical Analysis ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Cell Infection ◽  
Globally Asymptotically Stable ◽  
Single Strain ◽  
Density Dependent ◽  
Number Formula

In this paper, certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion are investigated. For the viral model with a single strain, we have proved the well-posedness and studied the global stabilities of equilibria by defining the basic reproductive number [Formula: see text] and structuring proper Lyapunov functional. Moreover, we found that the infection-free equilibrium is globally asymptotically stable if [Formula: see text], and the infection equilibrium is globally asymptotically stable if [Formula: see text]. For the multi-strain model, we found that all viral strains coexist if the corresponding basic reproductive number [Formula: see text], while virus will extinct if [Formula: see text]. As a result, we found that delay and the density-dependent diffusion does not influence the global stability of the model with cell-to-cell infection and homogeneous Neumann boundary conditions.

scholarly journals Analysis of a HBV Model with Diffusion and Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Noé Chan Chí ◽  
Eric ÁvilaVales ◽  
Gerardo García Almeida
Keyword(s):  
Reproduction Number ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Spatial Diffusion ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
B Virus ◽  
Comparison Arguments ◽  
Hbv Model ◽  
Iteration Technique

This paper discussed a hepatitis B virus infection with delay, spatial diffusion, and standard incidence function. The local stability of equilibrium is obtained via characteristic equations. By using comparison arguments, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproductive number is greater than unity, by means of an iteration technique, sufficiently conditions are obtained for the global asymptotic stability of the infected steady state. Numerical simulations are carried out to illustrate our findings.

scholarly journals Predicted impact of vaccination and active case finding measures to control epidemic of Coronavirus Disease 2019 (COVID-19) in a migrant-populated area in Thailand

2021 ◽  
Author(s):  
Rapeepong Suphanchaimat ◽  
Natthaprang Nittayasoot ◽  
Panithee Thammawijaya ◽  
Pard Teekasap ◽  
Kamnuan Ungchusak
Keyword(s):  
Vaccination Coverage ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Initial Population ◽  
Deterministic System ◽  
Single Measure ◽  
Vaccination Strategies ◽  
Epidemic Area ◽  
The Impact ◽  
Second Wave

Abstract Background: Thailand experienced the first wave of Coronavirus Disease 2019 (COVID-19) during March-May 2020 and was now facing the second wave of COVID-19 since December 2020. For the second wave, the intensity was more pronounced. The area faced the greatest hit was Samut Sakhon, a main migrant-receiving province in the country. Thus, the Thai Ministry of Public Health (MOPH) was now considering the initiation of vaccination strategies in combination with active face finding (ACF) in the epidemic area. The objective of this study was to assess the impact of various vaccination and ACF policy scenarios in terms of case reduction and deaths averted.Methods: The study obtained data mainly from the Division of Epidemiology, Department of Disease Control (DDC), MOPH. Deterministic system dynamics and compartmental models were exercised. Basic reproductive number (R0) was estimated at 3 from the beginning. Vaccine efficacy against disease transmission was assumed to be 50%. A total of 10,000 people were estimated as an initial population size.Results: The findings showed that the greater the vaccination coverage was, the smaller the size of incident and cumulative cases. Compared with no-vaccination and no-ACF scenario, the 90%-vaccination coverage combined with 90%-ACF coverage contributed a reduction of cumulative cases by 33%. The case reduction benefit would be greater when R0 was smaller (⁓53% and ⁓51% when R0 equated 2 and 1.5 respectively).Conclusion: This study reaffirmed the idea that a combination of vaccination and ACF measures contributed to favourable results in reducing the number of COVID-19 cases and deaths, relative to the implementation of only a single measure. The greater the vaccination and ACF coverage was, the greater the volume of cases could be saved. Though we demonstrated the benefit of vaccination strategies in this setting, the actual implementation needs to consider many more policy angles, such as social acceptability, cost-effectiveness and operational feasibility. Further studies that address these topics based on empirical evidence are of great value.

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