Intrinsic definitions of "relative velocity" in general relativity

Given two observers, we define the "relative velocity" of one observer with respect to the other in four different ways. All four definitions are given intrinsically, i.e. independently of any coordinate system. Two of them are given in the framework of spacelike simultaneity and, analogously, the other two are given in the framework of observed (lightlike) simultaneity. Properties and physical interpretations are discussed. Finally, we study relations between them in special relativity, and we give some examples in Schwarzschild and Robertson-Walker spacetimes.Comment: 29 pages, 12 figures. New proofs in special relativity and a new open problem in general relativity (see Remark 5.2). An Appendix has been added, studying the relative velocities in Schwarzschild, with new figures. Some spelling erros fixe

Migration paths saturations in meta-epidemic systems

In this paper we consider a simple two-patch model in which a population affected by a disease can freely move. We assume that the capacity of the interconnected paths is limited, and thereby influencing the migration rates. Possible habitat disruptions due to human activities or natural events are accounted for. The demographic assumptions prevent the ecosystem to be wiped out, and the disease remains endemic in both populated patches at a stable equilibrium, but possibly also with an oscillatory behavior in the case of unidirectional migrations. Interestingly, if infected cannot migrate, it is possible that one patch becomes disease-free. This fact could be exploited to keep disease-free at least part of the population

Height and risk of death among men and women: aetiological implications of associations with cardiorespiratory disease and cancer mortality

OBJECTIVES: Height is inversely associated with cardiovascular disease mortality risk and has shown variable associations with cancer incidence and mortality. The interpretation of findings from previous studies has been constrained by data limitations. Associations between height and specific causes of death were investigated in a large general population cohort of men and women from the West of Scotland. DESIGN: Prospective observational study. SETTING: Renfrew and Paisley, in the West of Scotland. SUBJECTS: 7052 men and 8354 women aged 45-64 were recruited into a study in Renfrew and Paisley, in the West of Scotland, between 1972 and 1976. Detailed assessments of cardiovascular disease risk factors, morbidity and socioeconomic circumstances were made at baseline. MAIN OUTCOME MEASURES: Deaths during 20 years of follow up classified into specific causes. RESULTS: Over the follow up period 3347 men and 2638 women died. Height is inversely associated with all cause, coronary heart disease, stroke, and respiratory disease mortality among men and women. Adjustment for socioeconomic position and cardiovascular risk factors had little influence on these associations. Height is strongly associated with forced expiratory volume in one second (FEV1) and adjustment for FEV1 considerably attenuated the association between height and cardiorespiratory mortality. Smoking related cancer mortality is not associated with height. The risk of deaths from cancer unrelated to smoking tended to increase with height, particularly for haematopoietic, colorectal and prostate cancers. Stomach cancer mortality was inversely associated with height. Adjustment for socioeconomic position had little influence on these associations. CONCLUSION: Height serves partly as an indicator of socioeconomic circumstances and nutritional status in childhood and this may underlie the inverse associations between height and adulthood cardiorespiratory mortality. Much of the association between height and cardiorespiratory mortality was accounted for by lung function, which is also partly determined by exposures acting in childhood. The inverse association between height and stomach cancer mortality probably reflects Helicobacter pylori infection in childhood resulting inor being associated withshorter height. The positive associations between height and several cancers unrelated to smoking could reflect the influence of calorie intake during childhood on the risk of these cancers

Epidemiological impact of waning immunization on a vaccinated population

This is an epidemiological SIRV model based study that is de- signed to analyze the impact of vaccination in containing infection spread, in a 4-tiered population compartment comprised of susceptible, infected, recov- ered and vaccinated agents. While many models assume a lifelong protection through vaccination, we focus on the impact of waning immunization due to conversion of vaccinated and recovered agents back to susceptible ones. Two asymptotic states exist, the \disease-free equilibrium" and the \endemic equi- librium" and we express the transitions between these states as function of the vaccination and conversion rates and using the basic reproduction number. We nd that the vaccination of newborns and adults have dierent consequences on controlling an epidemic. Also, a decaying disease protection within the re- covered sub-population is not sucient to trigger an epidemic on the linear level. We perform simulations for a parameter set modelling a disease with waning immunization like pertussis. For a diusively coupled population, a transition to the endemic state can proceed via the propagation of a traveling infection wave, described successfully within a Fisher-Kolmogorov framework

Covid-19 Mortality Rates in Northamptonshire UK: Initial Sub-regional Comparisons and Provisional SEIR model of First Wave Disease Spread

We analysed mortality rates in a non-metropolitan UK subregion (Northamptonshire) using statistically-weighted data fitted to the start of the epidemic to quantify SARS-CoV-2 disease fatalities at sub 1,000,000 population levels. Using parameter estimates derived from the recorded mortality data, a numerical (SEIR) model was developed to predict the spread of Covid-19 sub regionally. Model outputs, including analysis of transmission rates and the basic reproduction number, suggest national lockdown flattened the curve and reduced potential deaths by up to 4000 locally. The modelled number of infected and recovered individuals is higher than official estimates, and a revised form of the theoretical critical population fraction requiring immunisation is derived. Combining published (sub-regional) mortality rate data with deterministic models on disease spread has the potential to help public health practitioners refine bespoke mitigation plans guided by local population demographics

Epidemic centrality - is there an underestimated epidemic impact of network peripheral nodes?

In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as "superspreaders", are associated to dominant epidemic risks and therefore deserve special attention. In simulations on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dependence is illustrated in an analytically tractable example. In systems where the allocation of resources to counter disease spreading to individual nodes is based on their ranking, the dynamical regime of disease spreading is frequently not known before the outbreak of the disease. Therefore, we introduce a quantity called epidemic centrality as an average over all relevant regimes of disease spreading as a basis of the ranking. A recently introduced concept of phase diagram of epidemic spreading is used as a framework in which several types of averaging are studied. The epidemic centrality is compared to structural properties of nodes such as node degree, k-cores and betweenness. There is a growing trend of epidemic centrality with degree and k-cores values, but the variation of epidemic centrality is much smaller than the variation of degree or k-cores value. It is found that the epidemic centrality of the structurally peripheral nodes is of the same order of magnitude as the epidemic centrality of the structurally central nodes. The implications of these findings for the distributions of resources to counter disease spreading are discussed

A simple model to quantitatively account for periodic outbreaks of the measles in the Dutch Bible Belt

In the Netherlands there has been nationwide vaccination against the measles since 1976. However, in small clustered communities of orthodox Protestants there is widespread refusal of the vaccine. After 1976, three large outbreaks with about 3000 reported cases of the measles have occurred among these orthodox Protestants. The outbreaks appear to occur about every twelve years. We show how a simple Kermack-McKendrick-like model can quantitatively account for the periodic outbreaks. Approximate analytic formulae to connect the period, size, and outbreak duration are derived. With an enhanced model we take the latency period in account. We also expand the model to follow how different age groups are affected. Like other researchers using other methods, we conclude that large scale underreporting of the disease must occur