作者机构：
[Zhang, Xing An; Yin, Hong Yan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Yin, Hong Yan] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.;[Zhou, Da] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.
通讯机构：
[Zhang, Xing An] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
In this paper, we investigate the isolated closed orbits of two types of cubic vector fields in Double-struck capital R-3 by using the idea of central projection transformation, which sets up a bridge connecting the vector field X (x) in Double-struck capital R-3 with the planar vector fields. We have proved that the cubic vector field in Double-struck capital R-3 can have two isolated closed orbits or one closed orbit on the invariant cone. As an application of this result, we have shown that a class of 3-dimensional cubic system has at least 10 isolated closed orbits located on 5 invariant cones, and another type of 3-dimensional cubic system has at least 26 isolated closed orbits located on 13 invariant cones or 26 invariant cones.
关键词：
General nonlinear incidence rate;Relapse;Media impact;Global stability;Varying total population size
摘要：
The aim of this paper is to extend the incidence rate of an SEIR epidemic model with relapse and varying total population size to a general nonlinear form, which does not only include a wide range of monotonic and concave incidence rates but also takes on some neither monotonic nor concave cases, which may be used to reflect media education or psychological effect. By application of the novel geometric approach based on the third additive compound matrix, we focus on establishing the global stability of the SEIR model. Our analytical results reveal that the model proposed can retain its threshold dynamics that the basic reproduction number completely determines the global stability of equilibria. Our conclusions are applied to two special incidence functions reflecting media impact.
作者机构：
[Li, Yong; Liu, Xianning] Southwest Univ, Minist Educ, Sch Math & Stat, Key Lab Ecoenvironm Three Gorges Reservoir Reg, Chongqing 400715, Peoples R China.;[Li, Yong] Yangtze Univ, Sch Informat & Math, Jingzhou 434023, Peoples R China.;[Wang, Lianwen] Hubei Univ Nationalities, Dept Math, Enshi 445000, Peoples R China.;[Zhang, Xingan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Liu, Xianning] S;Southwest Univ, Minist Educ, Sch Math & Stat, Key Lab Ecoenvironm Three Gorges Reservoir Reg, Chongqing 400715, Peoples R China.
关键词：
Scarlet fever;behavior and habits;nonlinear incidence;Hopf bifurcation;data fitting
摘要：
An SIRS epidemic model incorporating incubation time delay and novel nonlinear incidence is proposed and analyzed to seek for the control strategies of scarlet fever, where the contact rate which can reflect the regular behavior and habit changes of children is non-monotonic with respect to the number of susceptible. The model without delay may exhibit backward bifurcation and bistable states even though the basic reproduction number is less than unit. Furthermore, we derive the conditions for occurrence of Hopf bifurcation when the time delay is considered as a bifurcation parameter. The data of scarlet fever of China are simulated to verify our theoretical results. In the end, several effective preventive and intervention measures of scarlet fever are found out.
摘要：
Biological experimental data normally contain noise due to probabilistic character of biochemical reactions and environmental fluctuations. It has been widely assumed that the observed data is the corresponding system states plus a white noise whose variance is a constant. In addition, all observations are assumed to be independent to each other. However, recently biological studies suggested that the randomness in experimental data may depend on system state and observations of different variables may be highly correlated. To address these issues, this work proposes a new model in which the variance of noise is a function of system state. We design a copula particle filter algorithm that is characterized by using copula density functions in place of multivariable normal density functions. The combination of the noise model and copula particle filter leads to a novel algorithm whose performance is rigorously evaluated by inferring unknown parameters in mathematical models. We test three linear/nonlinear functions to fit the noisy data and numerical results suggest that the nonlinear sigmoid function is the best function to represent the state-dependent variance of noise. Our proposed method has better accuracy of estimated parameters than the widely use the Liu-West filter and copula particle filter algorithm. Numerical results suggest that our proposed method is superior to the other two widely filter algorithms and is very effective for parameter estimation in biochemical network models under noisy dependent observations.
摘要：
In this work, in order to identify the most effective measure and combinations of several measures to control influenza spread, we propose an SVEIAR influenza model with imperfect vaccination, media coverage and antiviral treatment. The global dynamics of the model is explored. Sensitivity analysis of the basic reproduction number and the endemic equilibrium is conducted to evaluate the effectiveness of influenza control measures. Furthermore, an optimal control problem incorporating the three measures is formulated to design optimal control strategies for influenza. The cost-effectiveness analysis reveals that combining the three measures is the most cost-effective among the strategies considered. Numerical simulations show that media propaganda can play a dominant role in curbing influenza transmission.
关键词：
Incomplete vaccination;Age-dependent vaccination and latency;SVEIR model;Media-induced nonlinear incidence;Global stability;Lyapunov function
摘要：
Some studies show that the efficacy of vaccines may decline and the vaccine-induced immunity wanes with time elapsed since vaccination (e.g., BCG, HBV vaccines). Meanwhile, the use of media can effectively contain the emerging epidemics. In our work, an SVEIR epidemic model with media impact, age-dependent vaccination and latency is proposed, where the efficacy of vaccines depends on the time since vaccination. Uniform persistence and the sharp threshold dynamics are established, that is, the vaccination reproduction number completely determines the global dynamics of the model system. Our main results established can be extended to the SVEIR model with the general nonlinear infectious force function of monotonicity and concavity.
期刊：
Journal of Theoretical Biology,2016年390:40-49 ISSN：0022-5193
通讯作者：
Zhou, Da;Zhang, Xingan
作者机构：
[Zhang, Xingan; Chen, Xiufang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhou, Da] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.;[Wang, Yue] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA.;[Feng, Tianquan] Nanjing Normal Univ, Sch Teachers Educ, Nanjing 210023, Jiangsu, Peoples R China.;[Yi, Ming] Huazhong Agr Univ, Dept Phys, Coll Sci, Wuhan 430070, Hubei, Peoples R China.
通讯机构：
[Zhou, Da] X;[Zhang, Xingan] C;Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still questionable if the phenotypic plasticity is a crucial improvement to the hierarchical model or just a minor extension to it, it is worthwhile to explore the dynamic behavior characterizing the reversible phenotypic plasticity. In this study we compare the hierarchical model and the reversible model in predicting the cell-state dynamics observed in biological experiments. Our results show that the hierarchical model shows significant disadvantages over the reversible model in describing both long-term stability (phenotypic equilibrium) and short-term transient dynamics (overshoot) in cancer cell populations. In a very specific case in which the total growth of population due to each cell type is identical, the hierarchical model predicts neither phenotypic equilibrium nor overshoot, whereas the reversible model succeeds in predicting both of them. Even though the performance of the hierarchical model can be improved by relaxing the specific assumption, its prediction to the phenotypic equilibrium strongly depends on a precondition that may be unrealistic in biological experiments. Moreover, it still does not show as rich dynamics as the reversible model in capturing the overshoots of both CSCs and non-CSCs. By comparison, it is more likely for the reversible model to correctly predict the stability of the phenotypic mixture and various types of overshoot behavior.
摘要：
An SVEIR epidemic model with imperfect vaccination and nonlinear incidence, and a general latent distribution is formulated. By constructing Lyapunov functionals, it is shown that the disease will die out if the vaccination reproduction number R-vac <= 1 and the disease becomes endemic if R-vac > 1. Furthermore, vaccination effects are analyzed. Two special forms the probability of remaining in latent class are discussed. When the probability is negatively exponentially distributed, we present an efficient approach of proving global stability of the endemic equilibrium of the SVEIR system of ordinary differential equations (ODEs), which may improve some known approaches. When the probability is a step-function, the delay differential equation (DDE) system derived is used to study the impacts of vaccination and saturated incidence on the mumps transmission. (C) 2016 Elsevier Inc. All rights reserved.
