A probability generating function method for stochastic reaction networks

In this paper we present a probability generating function (PGF) approach for analyzing stochastic reaction networks. The master equation of the network can be converted to a partial differential equation for PGF. Using power series expansion of PGF and Pade approximation, we develop numerical schemes for finding probability distributions as well as first and second moments. We show numerical accuracy of the method by simulating chemical reaction examples such as a binding-unbinding reaction, an enzyme-substrate model, Goldbeter-Koshland ultrasensitive switch model, and G(2)/M transition model.open1

Epidemic Spreading in Complex Networks with Resilient Nodes: Applications to FMD

At the outbreak of the animal epidemic disease, farms that recover quickly from partially infected state can delay or even suppress the wide spreading of the infection over farm networks. In this work, we focus on how the spatial transmission of the infection is affected by both factors, the topology of networks and the internal resilience mechanism of nodes. We first develop an individual farm model to examine the influence of initial number of infected individuals and vaccination rate on the transmission in a single farm. Based on such intrafarm model, the farm network is constructed which reflects disease transmission between farms at various stages. We explore the impact of the farms vaccinated at low rates on the disease transmission into entire farm network and investigate the effect of the control on hub farms on the transmission over the farm network. It is shown that intensive control on the farms vaccinated at low rates and hub farms effectively reduces the potential risk of foot-and-mouth disease (FMD) outbreak on the farm network

Solution Interpolation Method for Highly Oscillating Hyperbolic Equations

This paper deals with a novel numerical scheme for hyperbolic equations with rapidly changing terms. We are especially interested in the quasilinear equation u(t) + au(x). = f(x)u + g(x)u(n) and the wave equation u(tt) = f(x)u(xx) that have a highly oscillating term like f(x) = sin(x/epsilon), epsilon << 1. It also applies to the equations involving rapidly changing or even discontinuous coefficients. The method is based on the solution interpolation and the underlying idea is to establish a numerical scheme by interpolating numerical data with a parameterized solution of the equation. While the constructed numerical schemes retain the same stability condition, they carry both quantitatively and qualitatively better performances than the standard method.open0

Potential effects of climate change on dengue transmission dynamics in Korea

Dengue fever is a major international public health concern, with more than 55% of the world population at risk of infection. Recent climate changes related to global warming have increased the potential risk of domestic outbreaks of dengue in Korea. In this study, we develop a two-strain dengue model associated with climate-dependent parameters based on Representative Concentration Pathway (RCP) scenarios provided by the Korea Meteorological Administration. We assess the potential risks of dengue outbreaks by means of the vector capacity and intensity under various RCP scenarios. A sensitivity analysis of the temperature-dependent parameters is performed to explore the effects of climate change on dengue transmission dynamics. Our results demonstrate that a higher temperature significantly enhances the potential threat of domestic dengue outbreaks in Korea. Furthermore, we investigate the effects of countermeasures on the cumulative incidence of humans and vectors. The current main control measures (comprising only travel restrictions) for infected humans in Korea are not as effective as combined control measures (travel restrictions and vector control), dramatically reducing the possibilities of dengue outbreaks

A moment closure method for stochastic reaction networks

In this paper we present a moment closure method for stochastically modeled chemical or biochemical reaction networks. We derive a system of differential equations which describes the dynamics of means and all central moments from a chemical master equation. Truncating the system for the central moments at a certain moment term and using Taylor approximation, we obtain explicit representations of means and covariances and even higher central moments in recursive forms. This enables us to deal with the moments in successive differential equations and use conventional numerical methods for their approximations. Furthermore, we estimate the errors in the means and central moments generated by the approximation method. We also find the moments at equilibrium by solving truncated algebraic equations. We show in examples that numerical solutions based on the moment closure method are accurate and efficient by comparing the results to those of stochastic simulation algorithms.open303

Chronic Inflammation in the Epidermis: A Mathematical Model

The epidermal tissue is the outmost component of the skin that plays an important role as a first barrier system in preventing the invasion of various environmental agents, such as bacteria. Recent studies have identified the importance of microbial competition between harmful and beneficial bacteria and the diversity of the skin surface on our health. We develop mathematical models (M1 and M2 models) for the inflammation process using ordinary differential equations and delay differential equations. In this paper, we study microbial community dynamics via transcription factors, protease and extracellular cytokines. We investigate possible mechanisms to induce community composition shift and analyze the vigorous competition dynamics between harmful and beneficial bacteria through immune activities. We found that the activation of proteases from the transcription factor within a cell plays a significant role in the regulation of bacterial persistence in the M1 model. The competition model (M2) predicts that different cytokine clearance levels may lead to a harmful bacteria persisting system, a bad bacteria-free state and the co-existence of harmful and good bacterial populations in Type I dynamics, while a bi-stable system without co-existence is illustrated in the Type II dynamics. This illustrates a possible phenotypic switch among harmful and good bacterial populations in a microenvironment. We also found that large time delays in the activation of immune responses on the dynamics of those bacterial populations lead to the onset of oscillations in harmful bacteria and immune activities. The mathematical model suggests possible annihilation of time-delay-driven oscillations by therapeutic drugs.ope