PROC
Synchronized and nonsymmetric phase-locked periodic solutions in a neteork of neurons with McCulloch-Pitts nonlinearity
Yuming Chen
Conference Publications 2001, 2001(Special): 102-108 doi: 10.3934/proc.2001.2001.102
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keywords:
MBE
An age-structured vector-borne disease model with horizontal transmission in the host
Xia Wang Yuming Chen
Mathematical Biosciences & Engineering 2018, 15(5): 1099-1116 doi: 10.3934/mbe.2018049

We concern with a vector-borne disease model with horizontal transmission and infection age in the host population. With the approach of Lyapunov functionals, we establish a threshold dynamics, which is completely determined by the basic reproduction number. Roughly speaking, if the basic reproduction number is less than one then the infection-free equilibrium is globally asymptotically stable while if the basic reproduction number is larger than one then the infected equilibrium attracts all solutions with initial infection. These theoretical results are illustrated with numerical simulations.

keywords: Vector-borne disease infection age global stability global attractor Lyapunov functional
MBE
An SIRS model with differential susceptibility and infectivity on uncorrelated networks
Maoxing Liu Yuming Chen
Mathematical Biosciences & Engineering 2015, 12(3): 415-429 doi: 10.3934/mbe.2015.12.415
We propose and study a model for sexually transmitted infections on uncorrelated networks, where both differential susceptibility and infectivity are considered. We first establish the spreading threshold, which exists even in the infinite networks. Moreover, it is possible to have backward bifurcation. Then for bounded hard-cutoff networks, the stability of the disease-free equilibrium and the permanence of infection are analyzed. Finally, the effects of two immunization strategies are compared. It turns out that, generally, the targeted immunization is better than the proportional immunization.
keywords: uncorrelated network Sexually transmitted infection spreading threshold permanence.
DCDS-B
Optimal contraception control for a nonlinear population model with size structure and a separable mortality
Rong Liu Feng-Qin Zhang Yuming Chen
Discrete & Continuous Dynamical Systems - B 2016, 21(10): 3603-3618 doi: 10.3934/dcdsb.2016112
This paper is concerned with the problem of optimal contraception control for a nonlinear population model with size structure. First, the existence of separable solutions is established, which is crucial in obtaining the optimal control strategy. Moreover, it is shown that the population density depends continuously on control parameters. Then, the existence of an optimal control strategy is proved via compactness and extremal sequence. Finally, the conditions of the optimal strategy are derived by means of normal cones and adjoint systems.
keywords: adjoint system normal cone contraception control separable mortality. Size structure
MBE
The global stability of an SIRS model with infection age
Yuming Chen Junyuan Yang Fengqin Zhang
Mathematical Biosciences & Engineering 2014, 11(3): 449-469 doi: 10.3934/mbe.2014.11.449
Infection age is an important factor affecting the transmission of infectious diseases. In this paper, we consider an SIRS model with infection age, which is described by a mixed system of ordinary differential equations and partial differential equations. The expression of the basic reproduction number $\mathscr {R}_0$ is obtained. If $\mathscr{R}_0\le 1$ then the model only has the disease-free equilibrium, while if $\mathscr{R}_0>1$ then besides the disease-free equilibrium the model also has an endemic equilibrium. Moreover, if $\mathscr{R}_0<1$ then the disease-free equilibrium is globally asymptotically stable otherwise it is unstable; if $\mathscr{R}_0>1$ then the endemic equilibrium is globally asymptotically stable under additional conditions. The local stability is established through linearization. The global stability of the disease-free equilibrium is shown by applying the fluctuation lemma and that of the endemic equilibrium is proved by employing Lyapunov functionals. The theoretical results are illustrated with numerical simulations.
keywords: global stability persistence. SIRS model infection age
DCDS-B
Global dynamics of an age-structured HIV infection model incorporating latency and cell-to-cell transmission
Jinliang Wang Jiying Lang Yuming Chen
Discrete & Continuous Dynamical Systems - B 2017, 22(10): 3721-3747 doi: 10.3934/dcdsb.2017186

In this paper, we are concerned with an age-structured HIV infection model incorporating latency and cell-to-cell transmission. The model is a hybrid system consisting of coupled ordinary differential equations and partial differential equations. First, we address the relative compactness and persistence of the solution semi-flow, and the existence of a global attractor. Then, applying the approach of Lyapunov functionals, we establish the global stability of the infection-free equilibrium and the infection equilibrium, which is completely determined by the basic reproduction number.

keywords: HIV infection cell-to-cell transmission latency equilibrium global stability Lyapunov functional

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