We have developed a pair of stochastic simulation models that describe the daily dynamics of dengue

Huanglongbing (HLB) is a bacterial infection of citrus trees transmitted by the Asian citrus psyllid Diaphorina citri. Mitigation of HLB has focused on spraying of insecticides to reduce the psyllid population and removal of trees when they first show symptoms of the disease. These interventions have been only marginally effective, because symptoms of HLB do not appear on leaves for months to years after initial infection. Limited knowledge about disease spread during the asymptomatic phase is exemplified by the heretofore unknown length of time from initial infection of newly developing cluster of young leaves, called flush, by adult psyllids until the flush become infectious. We present experimental evidence showing that young flush become infectious within 15 d after receiving an inoculum of Candidatus Liberibacter asiaticus (bacteria). Using this critical fact, we specify a microsimulation model of asymptomatic disease spread and intensity in a grove of citrus trees. We apply a range of psyllid introduction scenarios to show that entire groves can become infected with up to 12,000 psyllids per tree in less than 1 y, before most of the trees show any symptoms. We also show that intervention strategies that reduce the psyllid population by 75% during the flushing periods can delay infection of a full grove, and thereby reduce the amount of insecticide used throughout a year. This result implies that psyllid surveillance and control, using a variety of recently available technologies, should be used from the initial detection of invasion and throughout the asymptomatic period.asymptomatic huanglongbing | latent period | transmission model | control strategies T he main symptoms of huanglongbing (HLB) in citrus trees are yellow shoots, leaves with blotchy mottle, and small lopsided fruits. Ultimately, infected branches die back and the tree dies. The putative causal agent of HLB is an alpha-proteobacterium, Candidatus Liberibacter asiaticus (Ca. Las), that resides within the phloem and is transmitted by the Asian citrus psyllid Diaphorina citri Kuwayama. The highest concentrations of Ca. Las in infected trees are in the stem and midribs of flush. The flush is a newly developing cluster of very young leaves on the expanding end of a terminal shoot. The bacterium multiplies in both the psyllids and the trees, but the psyllids are essential for the spread of the disease.The dominant control measure currently in use is the combination of insecticidal spraying to limit the psyllid populations and removal of infected trees, an inoculum source, when they are symptomatic. This strategy has had only marginal effect because symptoms appear anywhere from months to years after an initial infection, long after the trees have been active in the transmission process (1). Presymptomatic trees can serve as a source of inoculum for psyllids, but the length of time from initial infection of a tree until it is infective as a source of inoculum is known from experimental measurements only to within coarse bounds (within 60 d) (1). A...

An effective method is given for computing the Hausdorff dimension of the boundary of a self‐similar digit tile T in n‐dimensional Euclidean space: dimH(∂T)=logλlogc where 1/c is the contraction factor and λ is the largest eigenvalue of a certain contact matrix first defined by Gröchenig and Haas.

Topology 37 (1998) 791-803. doi:10.1016/S0040-9383(97)00048-7Received by publisher: 1996-10-20Harvest Date: 2016-01-04 12:20:53DOI: 10.1016/S0040-9383(97)00048-7Page Range: 791-80

BackgroundSmall populations that have been isolated by conflict make vaccination and surveillance difficult, threatening polio eradication. Silent circulation is caused by asymptomatic infections. It is currently not clear whether the dynamics of waning immunity also influence the risk of silent circulation in the absence of vaccination. Such circulation can, nevertheless, be present following a declaration of elimination as a result of inadequate acute flaccid paralysis surveillance (AFPS) or environmental surveillance (ES).MethodsWe have constructed a stochastic model to understand how stochastic effects alter the ability of small populations to sustain virus circulation in the absence of vaccination. We analyzed how the stochastic process determinants of the duration of silent circulation that could have been detected by ES were affected by R0, waning dynamics, population size, and AFPS sensitivity in a discrete individual stochastic model with homogeneous contagiousness and random mixing. We measured the duration of silent circulation both by the interval between detected acute flaccid paralysis (AFP) cases and the duration of circulation until elimination.ResultsAs R0 increased and population size increased, the interval between detected AFP cases and the duration of circulation until elimination increased. As AFPS detection rates decreased, the interval between detected AFP cases increased. There was up to a 22% chance of silent circulation lasting for more than 3 years with 100% AFP detection. The duration of silent circulation was not affected by the waning immunity dynamics.ConclusionWe demonstrated that small populations have the potential to sustain prolonged silent circulation. Surveillance in these areas should be intensified before declaring elimination. To further validate these conclusions, it is necessary to realistically relax the simplifying assumptions about mixing and waning.