To the Editor—Dominguez et al. [1] described outbreaks of measles occurring in Catalonia despite good vaccination rates. The way in which heterogeneity in the distribution of nonimmune individuals diminishes herd immunity can be explained using network simulation models. Herd immunity is the indirect impact of vaccination on an epidemic. This effect is caused by having a sufficient number of im...

Information about infectious disease outbreaks is often gathered indirectly, from doctor’s reports and health board records. It also typically underestimates the actual number of cases, but the relationship between the observed proxies and the numbers that drive the diseases is complicated, nonlinear and potentially timeand state-dependent. We use a combination of data collection from the 2009-...

Identifying the reproductive consequences of insect migration is critical to understanding its ecological and evolutionary significance. However, many empirical studies are seemingly contradictory, making recognition of unifying themes elusive and controversial. The beet webworm, Loxostege sticticalis L. is a long-range migratory pest of many crops in the northern temperate zone from 36 °N to 5...

In this paper, we rigorously analyse an ordinary differential equation system that models fighting the HIV-1 virus with a genetically modified virus. We show that when the basic reproduction ratio ℛ(0)<1, then the infection-free equilibrium E (0) is globally asymptotically stable; when ℛ(0)>1, E (0) loses its stability and there is the single-infection equilibrium E (s). If ℛ(0)∈(1, 1+δ) where ...

Most pathogens threatening to cause extinction of a host species are maintained on one or more reservoir hosts, in addition to the species that is threatened by disease. Further, most conventional host-pathogen theory assumes that transmission is related to host density, and therefore a pathogen should become extinct before its sole host. Tasmanian devil facial tumor disease is a recently emerg...

Ten Chios ewe lambs and 10 Damascus she-kids born in October-November and similar numbers born in February along with eight multiparous females from each species, were used to examine pubertal events and reproductive seasonality. Reproductive activity was monitored by determining serum progesterone concentrations once a week for 12 months. The mean date of onset of ovulation (puberty) in autumn...

Abstract. In this paper, the global dynamics of a class of HIV-1 infection models with different infection rates and latently infected cells are investigated. We first modify the basic virus infection model and propose two models with bilinear infection rate and saturation infection rate, respectively, which take HIV-1 latency into consideration, and then study a model with a general nonlinear ...

In this work, we study an epidemic model with vaccination and vertical transmission. We get the basic reproduction number R0 of the system and carry out a bifurcation analysis and obtain the conditions ensuring that the system exhibits backward bifurcation. Mathematics Subject Classification : 34C05, 92D25

We study the spread of sexually transmitted infections (STIs) and other infectious diseases on a dynamic network by using a branching process approach. The nodes in the network represent the sexually active individuals, while connections represent sexual partnerships. This network is dynamic as partnerships are formed and broken over time and individuals enter and leave the sexually active popu...

Recently, de-Camino-Beck and Lewis (Bull Math Biol 69:1341-1354, 2007) have presented a method that under certain restricted conditions allows computing the basic reproduction ratio R₀ in a simple manner from life cycle graphs, without, however, giving an explicit indication of these conditions. In this paper, we give various sets of sufficient and generically necessary conditions. To this end,...