In this paper we consider epidemic models of directly transmissible SIR (susceptible → infective → recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting either of households or of households and workplaces. We review most reproduction numbers defined in the literature for these models, including the basic reproducti...

In this paper we consider an age-duration-structured population model for HIV infection in a homosexual community. First we investigate the invasion problem to establish the basic reproduction ratio R(0) for the HIV/AIDS epidemic by which we can state the threshold criteria: The disease can invade into the completely susceptible population if R(0)>1, whereas it cannot if R(0)<1. Subsequently, w...

The basic reproduction ratio, R0, is a fundamental concept in epidemiology. It is defined as the total number of secondary infections brought on by a single primary infection, in a totally susceptible population. The value of R0 indicates whether a starting epidemic reaches a considerable part of the population and causes a lot of damage, or whether it remains restricted to a relatively small n...

We consider the dynamics of a mosquito-transmitted pathogen in a multi-patch Ross-Macdonald malaria model with mobile human hosts, mobile vectors, and a heterogeneous environment. We show the existence of a globally stable steady state, and a threshold that determines whether a pathogen is either absent from all patches, or endemic and present at some level in all patches. Each patch is charact...

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-...

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...

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