Solutions and positive solutions for some three-point boundary value problems
Wenying Feng
Conference Publications 2003, 2003(Special): 263-272 doi: 10.3934/proc.2003.2003.263
We will prove existence results for some three-point boundary value problems by applying a Gronwall inequality. Then, we establish the existence of at least one positive solution for a three-point boundary value problem where the nonlinearity involves the first derivative.
keywords: positive solution. Boundary value problem cone
Existence of positive solutions for second order differential equations arising from chemical reactor theory
Wenying Feng Guang Zhang Yikang Chai
Conference Publications 2007, 2007(Special): 373-381 doi: 10.3934/proc.2007.2007.373
In this paper, we study second-order differential equations that represent the steady state model in an adiabatic tubular chemical reactor. Theoretical results on existence and range of positive solutions are proved by applying a fixed point theorem. At the mean time, numerical solutions are obtained by computer programming. Results from mathematical analysis are compared with the numerical solutions.
keywords: numerical simulation. Steady state model fixed point theorem positive solution
Stability analysis on an economic epidemiological model with vaccination
Wisdom S. Avusuglo Kenzu Abdella Wenying Feng
Mathematical Biosciences & Engineering 2017, 14(4): 975-999 doi: 10.3934/mbe.2017051

In this paper, an economic epidemiological model with vaccination is studied. The stability of the endemic steady-state is analyzed and some bifurcation properties of the system are investigated. It is established that the system exhibits saddle-point and period-doubling bifurcations when adult susceptible individuals are vaccinated. Furthermore, it is shown that susceptible individuals also have the tendency of opting for more number of contacts even if the vaccine is inefficacious and thus causes the disease endemic to increase in the long run. Results from sensitivity analysis with specific disease parameters are also presented. Finally, it is shown that the qualitative behaviour of the system is affected by contact levels.

keywords: Dynamical system economic epidemiology equilibrium eigenvalue stability vaccination

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