On spatially explicit models of cholera epidemics

We generalize a recently proposed model for cholera epidemics that accounts for local communities of susceptibles and infectives in a spatially explicit arrangement of nodes linked by networks having different topologies. The vehicle of infection (Vibrio cholerae) is transported through the network links that are thought of as hydrological connections among susceptible communities. The mathematical tools used are borrowed from general schemes of reactive transport on river networks acting as the environmental matrix for the circulation and mixing of waterborne pathogens. Using the diffusion approximation, we analytically derive the speed of propagation for travelling fronts of epidemics on regular lattices (either one-dimensional or two-dimensional) endowed with uniform population density. Power laws are found that relate the propagation speed to the diffusion coefficient and the basic reproduction number. We numerically obtain the related, slower speed of epidemic spreading for more complex, yet realistic river structures such as Peano networks and optimal channel networks. The analysis of the limit case of uniformly distributed population sizes proves instrumental in establishing the overall conditions for the relevance of spatially explicit models. To that extent, the ratio between spreading and disease outbreak time scales proves the crucial parameter. The relevance of our results lies in the major differences potentially arising between the predictions of spatially explicit models and traditional compartmental models of the susceptible–infected–recovered (SIR)-like type. Our results suggest that in many cases of real-life epidemiological interest, time scales of disease dynamics may trigger outbreaks that significantly depart from the predictions of compartmental models.     

一类具有Beverton-Holt出生函数的阶段结构传染病模型的全局分析

针对一些疾病仅在成年个体间传播和成年个体的成长受到密度制约等因素,建立了一类具有幼年和成年两个阶段且疾病仅在成年个体间传播的传染病模型,其中以具有饱和性质的Beverton-Holt函数作为幼年出生函数．通过构造恰当的Lyapunov函数和定性分析,得到了模型的全局动力学性态,并确定了决定模型动力学性态的种群存活的基本再生数和疾病传播的基本再生数．所得结果表明：当种群的基本再生数不大于 1 时,种群灭绝;当种群的基本再生数大于 1 而疾病传播的基本再生数不大于 1 时,种群持续生存而疾病灭绝;当疾病传播的基本再生数大于 1 时,种群持续存活且疾病会发展成地方病．     

Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic influenza: scenarios for the US, UK and the Netherlands

An increasing number of avian flu cases in humans, arising primarily from direct contact with poultry, in several regions of the world have prompted the urgency to develop pandemic preparedness plans worldwide. Leading recommendations in these plans include basic public health control measures for minimizing transmission in hospitals and communities, the use of antiviral drugs and vaccination. This paper presents a mathematical model for the evaluation of the pandemic flu preparedness plans of the United States (US), the United Kingdom (UK) and the Netherlands. The model is used to assess single and combined interventions. Using data from the US, we show that hospital and community transmission control measures alone can be highly effective in reducing the impact of a potential flu pandemic. We further show that while the use of antivirals alone could lead to very significant reductions in the burden of a pandemic, the combination of transmission control measures, antivirals and vaccine gives the most 'optimal' result. However, implementing such an optimal strategy at the onset of a pandemic may not be realistic. Thus, it is important to consider other plausible alternatives. An optimal preparedness plan is largely dependent on the availability of resources; hence, it is country-specific. We show that countries with limited antiviral stockpiles should emphasize their use therapeutically (rather than prophylactically). However, countries with large antiviral stockpiles can achieve greater reductions in disease burden by implementing them both prophylactically and therapeutically. This study promotes alternative strategies that may be feasible and attainable for the US, UK and the Netherlands. It emphasizes the role of hospital and community transmission control measures in addition to the timely administration of antiviral treatment in reducing the burden of a flu pandemic. The latter is consistent with the preparedness plans of the UK and the Netherlands. Our results indicate that for low efficacy and coverage levels of antivirals and vaccine, the use of a vaccine leads to the greatest reduction in morbidity and mortality compared with the singular use of antivirals. However, as these efficacy and coverage levels are increased, the use of antivirals is more effective.     

Invasion,persistence and control in epidemic models for plant pathogens: the effect of host demography

Many epidemiological models for plant disease include host demography to describe changes in the availability of susceptible tissue for infection. We compare the effects of using two commonly used formulations for host growth, one linear and the other nonlinear, upon the outcomes for invasion, persistence and control of pathogens in a widely used, generic model for botanical epidemics. The criterion for invasion, reflected in the basic reproductive number, R₀, is unaffected by host demography: R₀ is simply a function of epidemiological parameters alone. When, however, host growth is intrinsically nonlinear, unexpected results arise for persistence and the control of disease. The endemic level of infection (I_∞) also depends upon R₀. We show, however, that the sensitivity of I_∞ to changes in R₀ > 1 depends upon which underlying epidemiological parameter is changed. Increasing R₀ by shortening the infectious period results in a monotonic increase in I_∞. If, however, an increase in R₀ is driven by increases in transmission rates or by decreases in the decay of free-living inoculum, I_∞ first increases (R₀ < 2), but then decreases (R₀ > 2). This counterintuitive result means that increasing the intensity of control can result in more endemic infection.     

柔性隔振系统功率流特性及最优化控制策略

针对实际工程中力和力矩复杂激励下柔性耦全系统的隔振问题，综合考虑弹簧的纵向和横向刚度，运用导纳矩阵法推导了主动控制力下系统的动态传递方程。分析了力的对称性及弹簧刚度对传递到基础的功率流的影响，探讨了最优化控制的效果。     

不确定性控制系统的成因、分类与控制策略

分析了不确定性产生的各种因素和控制系统中不确定性的具体来源,给出了不确定性控制系统的分类,并分析了研究不确定性控制系统的若干控制策略。