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

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...

Livestock disease controls are often linked to movements between farms, for example, via quarantine and pre- or post-movement testing. Designing effective controls, therefore, benefits from accurate assessment of herd-to-herd transmission. Household models of human infections make use of R*, the number of groups infected by an initial infected group, which is a metapopulation level analogue of ...

Recent reviews (Feachem et al.; Alonso et al.) have concluded that in order to have a sustainable impact on the global burden of malaria, it is essential that we knowingly reduce the global incidence of infected persons. To achieve this we must reduce the basic reproductive rate of the parasites to < 1 in diverse epidemiological settings. This can be achieved by impacting combinations of the fo...

Little is known about the transmission dynamics of Acinetobacter baumannii in hospitals, despite such information being critical for designing effective infection control measures. In the absence of comprehensive epidemiological data, mathematical modelling is an attractive approach to understanding transmission process. The statistical challenge in estimating transmission parameters from infec...

We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential inf...