In this paper, we consider global stability for a heroin model with two distributed delays. The basic reproduction number of the heroin spread is obtained, which completely determine the stability of equilibria. Using the direct Lyapunov method with Volterra type Lyapunov function, we show that the drug use-free equilibrium is globally asymptotically stable if the basic reproduction number is l...

We discuss the epidemic network model with infectious force in latent and infected period. We obtain the basic reproduction number and analyze the globally dynamic behaviors of the diseasefree equilibrium when the basic reproduction number is less than one. The effects of various immunization schemes are studied. Finally, the final sizes relation is derived for the network epidemic model. The d...

A transmission model of malaria with two delays is formulated. We calculate the basic reproduction number R 0 for the model. It is shown that the basic reproduction number is a decreasing function of two time delays. The existence of the equilibria is studied. Our results suggest that the model undergoes a backward bifurcation, which implies that bringing the basic reproduction number below 1 i...

in recent years, preservation of fertility in women has been of great importance, especially in patients exposed to deleterious conditions on fertility. thus, cryopre-servation of human gametes, embryos and ovarian tissue has become an essential part of assisted reproduction. this approach limits the number of embryos transferred, while supernumerary oocytes and/ or embryos can be used in subse...

the present study was aimed to investigate the effect of fluoxetine on aggressive behaviors towards female and testosterone concentration of male fighting fish (betta splendens) during one reproduction event. male specimens were exposed 6 days to concentrations of 0 (control treatment) and 0.54 µg/l fluoxetine (exposed treatment) and aggressive behaviors of them assessed on different reproducti...

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...