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Dynamical analysis of a diffusive malaria model with fixed latent period in the human and vector populations 被引量:1
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作者 Hao Qu Tianli Jiang +1 位作者 Jinliang Wang Jiantao Zhao 《International Journal of Biomathematics》 SCIE 2023年第1期209-234,共26页
To investigate the impact of the fixed latent periods in the human and vector populations on the disease transmission in heterogenous environment,we formulate a nonlocal and time-delayed reaction-diffusion(NLTD-RD)sys... To investigate the impact of the fixed latent periods in the human and vector populations on the disease transmission in heterogenous environment,we formulate a nonlocal and time-delayed reaction-diffusion(NLTD-RD)system.By appealing to the next generation operator(NGO),we define the basic reproduction number(BRN)Ro,and prove it as a threshold parameter for indicating whether disease persists or not.Specifically,if o<1,the disease-free equilibrium is globally asymptotically stable,while if Ro>1,the disease is shown to be uniformly persistent.In the homogeneous case that all parameters are assumed to be constants,the explicit expression of o is obtained.We further achieved the global attractivity of the constant equilibria by utilizing Lyapunov functionals.Numerical simulations are performed to verify the theoretical results and the effects of the diffusion rate on disease transmission. 展开更多
关键词 Nonlocal delays spatial heterogeneity basic reproduction number uniform persistence Lyapunov functionals
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Quantization of a Class of Super W-Agebras
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作者 Yu Zhang Xiaomin Tang 《Algebra Colloquium》 SCIE CSCD 2022年第4期633-642,共10页
We study a class of super W-algebras whose even part is the Virasoro type Lie algebra W(2,2).We quantize the Lie superbialgebra of the super W-algebra by the Drinfeld twist quantization technique and obtain a class of... We study a class of super W-algebras whose even part is the Virasoro type Lie algebra W(2,2).We quantize the Lie superbialgebra of the super W-algebra by the Drinfeld twist quantization technique and obtain a class of noncommutative and noncocommutative Hopf superalgebras. 展开更多
关键词 QUANTIZATION super W-algebra quantum group Lie superbialgebra
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COEVOLUTIONARY DYNAMICS OF PREDATOR-PREY INTERACTIONS
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作者 MAN ZU JINLIANG WANG YASUHIRO TAKEUCHI 《International Journal of Biomathematics》 2012年第3期225-255,共31页
In this paper, with the method of adaptive dynamics, we investigate the coevolution of phenotypic traits of predator and prey species. The evolutionary model is constructed from a deterministic approximation of the un... In this paper, with the method of adaptive dynamics, we investigate the coevolution of phenotypic traits of predator and prey species. The evolutionary model is constructed from a deterministic approximation of the underlying stochastic ecological processes. Firstly, we investigate the ecological and evolutionary conditions that allow for continu- ously stable strategy and evolutionary branching. We find that evolutionary branching in the prey phenotype will occur when the frequency dependence in the prey carrying capacity is not strong. Furthermore, it is found that if the two prey branches move far away enough, the evolutionary branching in the prey phenotype will induce the sec- ondary branching in the predator phenotype. The final evolutionary outcome contains two prey and two predator species. Secondly, we show that under symmetric interactions the evolutionary model admits a supercritical Hopf bifurcation if the frequency depen- dence in the prey carrying capa.city is very weak. Evolutionary cycle is a likely outcome of the nmtation-selection processes. Finally, we find that frequency-dependent selection can drive the predator population to extinction under asymmetric interactions. 展开更多
关键词 Adaptive dynamics continuously stable strategy evolutionary branching BIODIVERSITY coevolution.
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DYNAMIC ANALYSIS OF AN SIR MODEL WITH STOCHASTIC PERTURBATIONS
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作者 ZHENJIE LIU JINLIANG WANG +1 位作者 YALAN XU GUOQIANG LI 《International Journal of Biomathematics》 2013年第6期63-77,共15页
In this paper, we present a differential infectivity SIR epidemic model with modified saturation incidences and stochastic perturbations. We show that the stochastic epidemic model has a unique global positive solutio... In this paper, we present a differential infectivity SIR epidemic model with modified saturation incidences and stochastic perturbations. We show that the stochastic epidemic model has a unique global positive solution, and we utilize stochastic Lyapunov functions to show the asymptotic behavior of the solution. 展开更多
关键词 Epidemiological model Ito's formula stochastic Lyapunov function asymptotic behavior.
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A MULTI-GROUP SVEIR EPIDEMIC MODEL WITH DISTRIBUTED DELAY AND VACCINATION 被引量:2
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作者 JINLIANG WANG YASUHIRO TAKEUCHI SHENGQIANG LIU 《International Journal of Biomathematics》 2012年第3期1-18,共18页
In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics a... In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination. 展开更多
关键词 Multi-group SVEIR model vaccination strategy global stability Lyapunovfunctionals graph theory.
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Stability analysis for delayed viral infection model with multitarget cells and general incidence rate
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作者 Jinliang Wang Xinxin Tian Xia Wang 《International Journal of Biomathematics》 2016年第1期135-155,共21页
In this paper, the sharp threshold properties of a (2n + 1)-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected tar- get cells, n classes of infected cells a... In this paper, the sharp threshold properties of a (2n + 1)-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected tar- get cells, n classes of infected cells and nonlinear incidence rate h(x,v). Two kinds of distributed time delays are incorporated into the model to describe the time needed for infection of uninfected target cells and virus replication. Under certain conditions, it is shown that the basic reproduction number is a threshold parameter for the existence of the equilibria, uniform persistence, as well as for global stability of the equilibria of the model. 展开更多
关键词 Viral infection model multitarget cells nonlinear incidence rate global stabi-lity Lyapunov functional.
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