具有饱和治疗的禽流感动力学模型的研究

提出了一类带有治疗的禽流感动力学模型,用来分析禽流感从禽类向人类传播的过程.由于治疗禽流感的药物十分有限,提出一个带有饱和治疗的模型.通过讨论得知当禽流感疫情已经发生时,通过控制染病的禽类就可抑制禽流感在人类的传播.     

Avian-human influenza epidemic model with diffusion

A diffusive epidemic model is investigated. This model describes the transmission of avian influenza among birds and humans. The behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions are investigated. Sufficient conditions for the local and global asymptotical stability are given by spectral analysis and by using Lyapunov functional. Our result shows that the disease-free equilibrium is globally asymptotically stable, if the contact rate for the susceptible birds and the contact rate for the susceptible humans are small. It suggests that the best policy to prevent the occurrence of a pandemic is not only to exterminate the infected birds with avian influenza but also to reduce the contact rate for susceptible humans with the individuals infected with mutant avian influenza. Numerical simulations are presented to illustrate the main results.     

Mathematical modelling of acute virus influenza A infections

This article models the immune system and the virus dynamics of acute influenza infection mathematically. We use the model to study the virus dynamics of some well-known and severe and mild types of viruses. Linkages to well-known models in the literature are illustrated. Simulations are compared with experimental results in vivo by comparing with results from infected ferrets where infection closely resembles those in humans. Good agreement is achieved between the model calculations and the experimental values for influenza A viruses. For the Spanish flu virus H1N1 peak virus load is high and virtually all cells are infected in the nostril. In general, the H1N1 viruses show much more prolonged infections than the H3N2 in the nostril. We suggest that the reason is that unspecific immunity attacks H3N2-budded viruses but not H1N1 viruses.     

Spreading and vanishing in a West Nile virus model with expanding fronts

We study a simplified version of a West Nile virus(WNv) model discussed by Lewis et al.(2006),which was considered as a first approximation for the spatial spread of WNv. The basic reproduction number R_0 for the non-spatial epidemic model is defined and a threshold parameter R_0~D for the corresponding problem with null Dirichlet boundary condition is introduced. We consider a free boundary problem with a coupled system, which describes the diffusion of birds by a PDE and the movement of mosquitoes by an ODE. The risk index R_0~F(t) associated with the disease in spatial setting is represented. Sufficient conditions for the WNv to eradicate or to spread are given. The asymptotic behavior of the solution to the system when the spreading occurs is considered. It is shown that the initial number of infected populations, the diffusion rate of birds and the length of initial habitat exhibit important impacts on the vanishing or spreading of the virus. Numerical simulations are presented to illustrate the analytical results.     

Numerical study of an influenza epidemic model with diffusion

A diffusive epidemic model is investigated with a view to describe the transmission of influenza as an epidemic. The equations are solved numerically using the splitting method under different initial distribution of population density. It is shown that the initial population distribution and diffusion play an important role for spread of disease. It is also shown that interventions (medical and nonmedical) significantly slow down the spread of disease. Stability of equilibria of the numerical solutions are also established.     

Numerical study of a diffusive epidemic model of influenza with variable transmission coefficient

A diffusive epidemic model for H1N1 influenza is formulated with a view to gain basic understanding of the virus behavior. All newborns are assumed to be susceptible. Mortality rate for infective individuals in the population is assumed to be greater than natural mortality rate. Latent, infectious and immune periods are assumed to be constants throughout this study. The numerical solutions of this model are carried out under three different initial populations distribution. In order to investigate the effect of the disease transmission coefficient on the spread of disease, β is taken to be constant as well as a function of seasonally varying time t and a function of spatial variable x  . The threshold quantity (_R0)$({\mathfrak{R}}_0)$ that governs the disease dynamics is derived. Numerical simulation shows that the system supports the existence of sustained and damped oscillations depending on initial populations distribution, the disease transmission rate and diffusion.     

Optimal control and sensitivity analysis of SIV→HIV dynamics with effects of infected immigrants in sub‐Saharan Africa

Regional migration has become an underlying factor in the spread of HIV transmission. In addition, immigrants with HIV status has contributed with high‐risk of sexually transmitted infection to its “destination” communities and promotes dissemination of HIV. Efforts to address HIV/AIDS among conflict‐affected populations should be properly addressed to eliminate potential role of the spread of the disease and risk of exposure to HIV. Motivated from this situation, HIV‐infected immigrants factor to HIV/SIV transmission link will be investigated in this research and examine its potential effect using optimal control method. Nonlinear deterministic mathematical model is used which is a multiple host model comprising of humans and chimpanzees. Some basic properties of the model such as invariant region and positivity of the solutions will be examined. The local stability of the disease‐free equilibrium was examined by computing the basic reproduction number, and it was found to be locally asymptotically stable when ?₀<1 and unstable otherwise. Sensitivity analysis was conducted to determine the parameters that help most in the spread of the virus. Pontryagin's maximum principle is used to obtain the optimality conditions for controlling the disease spread. Numerical simulation was conducted to obtain the analytical results. The results shows that combination of public health awareness, treatment, and culling help in controlling the HIV disease spread.     

Modelling the dynamics of avian influenza with nonlinear recovery rate and psychological effect

In this paper, a SI-SEIR type avian influenza epidemic model with psychological effect, nonlinear recovery rate and saturation inhibition effect is formulated to study the transmission and control of avian influenza virus. By setting the basic reproductive number as the threshold parameter and constructing Lyapunov function, Dulac function and using the Li-Muldowney''s geometry approach, we prove the local and global stability of disease-free equilibria and endemic equilibrium. Theoretical analysis are carried out to show the role of the saturation inhibition effect, psychological effect and effective medical resources in this model, and numerical simulations are also given to verify the results.     

The Fitting submodule

Let H be a finite group, a field and V a finite dimensional H-module. We introduce the Fitting submodule F_V (H), an H submodule of V which has properties similar to the generalized Fitting subgroup of a finite group. Received: 26 August 2005     

Simulating influenza pandemic dynamics with public risk communication and individual responsive behavior

Individual responsive behavior to an influenza pandemic has significant impacts on the spread dynamics of this epidemic. Current influenza modeling efforts considering responsive behavior either oversimplify the process and may underestimate pandemic impacts, or make other problematic assumptions and are therefore constrained in utility. This study develops an agent-based model for pandemic simulation, and incorporates individual responsive behavior in the model based on public risk communication literature. The resultant model captures the stochastic nature of epidemic spread process, and constructs a realistic picture of individual reaction process and responsive behavior to pandemic situations. The model is then applied to simulate the spread dynamics of 2009 H1N1 influenza in a medium-size community in Arizona. Simulation results illustrate and compare the spread timeline and scale of this pandemic influenza, without and with the presence of pubic risk communication and individual responsive behavior. Sensitivity analysis sheds some lights on the influence of different communication strategies on pandemic impacts. Those findings contribute to effective pandemic planning and containment, particularly at the beginning of an outbreak.     

Living with influenza: Impacts of government imposed and voluntarily selected interventions

Focusing on mitigation strategies for global pandemic influenza, we use elementary mathematical models to evaluate the implementation and timing of non-pharmaceutical intervention strategies such as travel restrictions, social distancing and improved hygiene. A spreadsheet model of infection spread between several linked heterogeneous communities is based on analytical calculations and Monte Carlo simulations. Since human behavior will likely change during the course of a pandemic, thereby altering the dynamics of the disease, we incorporate a feedback parameter into our model to reflect altered behavior. Our results indicate that while a flu pandemic could be devastating; there are coping methods that when implemented quickly and correctly can significantly mitigate the severity of a global outbreak.     

A fractional order epidemic model and simulation for avian influenza dynamics

We present a nonlinear fractional order epidemic model to investigate the spreading dynamical behavior of the avian influenza. The population of the model contains susceptible individuals, asymptomatic but infective latent individuals, and infective individuals. We first establish the existence, uniqueness, nonnegativity, and positive invariance of the solution, then we study the reproduction number of the model and the stability of the disease‐free equilibrium. We observe that the reproduction number varies with the order of the fractional derivative ν. In terms of epidemics, this suggests that varying ν induces a change in the avian's epidemic status. Furthermore, we derive the sufficient conditions for the existence and the stability of the endemic equilibrium. Finally, we carry out some numerical simulations to validate the analytical results. We find from simulations that the solution of the fractional order model tends to a stationary state over a longer period of time with decreasing the value of the fractional derivative, and the size of epidemic decreases with decreasing ν.     

An epidemic model to evaluate the homogeneous mixing assumption

Many epidemic models are written in terms of ordinary differential equations (ODE). This approach relies on the homogeneous mixing assumption; that is, the topological structure of the contact network established by the individuals of the host population is not relevant to predict the spread of a pathogen in this population. Here, we propose an epidemic model based on ODE to study the propagation of contagious diseases conferring no immunity. The state variables of this model are the percentages of susceptible individuals, infectious individuals and empty space. We show that this dynamical system can experience transcritical and Hopf bifurcations. Then, we employ this model to evaluate the validity of the homogeneous mixing assumption by using real data related to the transmission of gonorrhea, hepatitis C virus, human immunodeficiency virus, and obesity.     

Monotonicity,uniqueness, and stability of traveling waves in a nonlocal reaction‐diffusion system with delay

The purpose of this paper is to study the traveling wave solutions of a nonlocal reaction‐diffusion system with delay arising from the spread of an epidemic by oral‐faecal transmission. Under monostable and quasimonotone it is well known that the system has a minimal wave speed c* of traveling wave fronts. In this paper, we first prove the monotonicity and uniqueness of traveling waves with speed c ?c _?. Then we show that the traveling wave fronts with speed c >c _? are exponentially asymptotically stable.     

The spreading frontiers of avian-human influenza described by the free boundary

In this paper,a reaction-diffusion system is proposed to investigate avian-human influenza.Two free boundaries are introduced to describe the spreading frontiers of the avian influenza.The basic reproduction numbers rF0(t)and RF0(t)are defined for the bird with the avian influenza and for the human with the mutant avian influenza of the free boundary problem,respectively.Properties of these two time-dependent basic reproduction numbers are obtained.Sufficient conditions both for spreading and for vanishing of the avian influenza are given.It is shown that if rF0(0)<1 and the initial number of the infected birds is small,the avian influenza vanishes in the bird world.Furthermore,if rF0(0)<1 and RF0(0)<1,the avian influenza vanishes in the bird and human worlds.In the case that rF0(0)<1 and RF0(0)>1,spreading of the mutant avian influenza in the human world is possible.It is also shown that if rF0(t0)>1 for any t0>0,the avian influenza spreads in the bird world.     

Mutually permutable subgroups and Fitting classes

Let G = AB be the mutually permutable product of the subgroups A and B. It is shown that if A and B are contained in a Fitting class , then the commutator subgroup G′ of G is also contained in . Received: 14 August 2006 Revised: 17 September 2006     

A multi‐regional epidemic model for controlling the spread of Ebola: awareness,treatment, and travel‐blocking optimal control approaches

Ebola virus disease (EVD) can rapidly cause death to animals and people, for less than 1month. In addition, EVD can emerge in one region and spread to its neighbors in unprecedented durations. Such cases were reported in Guinea, Sierra Leone, and Liberia. Thus, by blocking free travelers, traders, and transporters, EVD has had also impacts on economies of those countries. In order to find effective strategies that aim to increase public knowledge about EVD and access to possible treatment while restricting movements of people coming from regions at high risk of infection, we analyze three different optimal control approaches associated with awareness campaigns, treatment, and travel‐blocking operations that health policy‐makers could follow in the war on EVD. Our study is based on the application of Pontryagin's maximum principle, in a multi‐regional epidemic model we devise here for controlling the spread of EVD. The model is in the form of multi‐differential systems that describe dynamics of susceptible, infected, and removed populations belonging to p different geographical domains with three control functions incorporated. The forward–backward sweep method with integrated progressive‐regressive Runge–Kutta fourth‐order schemes is followed for resolving the multi‐points boundary value problems obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

The analysis and application of an HBV model

A mathematical model is formulated to describe the spread of hepatitis B. The stability of equilibria and persistence of disease are analyzed. The results shows that the dynamics of the model is completely determined by the basic reproductive number ρ₀. If ρ₀ < 1, the disease-free equilibrium is globally stable. When ρ₀ > 1, the disease-free equilibrium is unstable and the disease is uniformly persistent. Furthermore, under certain conditions, it is proved that the endemic equilibrium is globally attractive. Numerical simulations are conducted to demonstrate our theoretical results. The model is applied to HBV transmission in China. The parameter values of the model are estimated based on available HBV epidemic data in China. The simulation results matches the HBV epidemic data in China approximately.     

Optimal control of dengue epidemic outbreaks under limited resources

In this paper, we reflect upon control intervention practices habitually exerted by healthcare authorities in tropical areas that suffer from incidental outbreaks of dengue fever, in particular, the city of Cali, Colombia. Such control interventions, principally based on the insecticide spraying, are carried out sporadically in order to overcome an ongoing epidemic or at least to reduce its size. It is worth pointing out that control actions of this type do not usually account for sufficient budget because epidemic outbreaks are difficult to predict. In practical terms, these occasional control interventions are performed by spraying, as quickly as possible, all existing stock of insecticide (regardless of its lethality) and employing all available manpower. The goal of this paper is to design better strategies for insecticide-based control actions, which are capable of preventing more human infections at no additional cost, and to reveal the obsolescence of current vector eradication practices. Our approach relies on dynamic optimization, where the number of averted human infections is maximized under budget constraint and subject to a simple dengue transmission model amended with one control variable that stands for the insecticide spraying. As a result, we obtain structurally robust control intervention policies that demonstrate better performance and higher resilience to possible budget limitations than traditional modus operandi.