In this paper, we introduce a basic reproduction number for a multigroup epidemic model with nonlinear incidence. Then, we establish that global dynamics are completely determined by the basic reproduction number R0. It shows that, the basic reproduction number R0 is a global threshold parameter in the sense that if it is less than or equal to one, the disease free equilibrium is globally stabl...

In this paper, we introduce a basic reproduction number for a multigroup SEIR model with nonlinear incidence of infection and nonlinear removal functions between compartments. Then, we establish that global dynamics are completely determined by the basic reproduction number R0. It shows that, the basic reproduction number R0 is a global threshold parameter in the sense that if it is less than o...

Trachoma programs have dramatically reduced the prevalence of the ocular chlamydia that cause the disease. Some have hypothesized that immunity to the infection may be reduced because of program success in reducing the incidence of infection, and transmission may then increase. Longitudinal studies of multiple communities would be necessary to test this hypothesis. Here, we quantify transmissio...

The feedback dynamics from mosquito to human and back to mosquito involve considerable time delays due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the human and the mosquito, we first propose a delayed Ross-Macdonald model. Then we calculate the basic reproduction number R0 and carry out some sensitivity analys...

We present new mathematical models that include the impact of using selected preventative measures such as insecticide treated nets (ITN) in controlling or ameliorating the spread of the Zika virus. For these models, we derive the basic reproduction number and sharp estimates for the final size relation. We first present a single-stage model which is later extended to a new multistage model for...

A continuous-time SIV (susceptible-infected-vaccinated) model of the transmission of Gonorrhea among homosexuals is analyzed. A basic reproduction number Ro is identified and it is shown that the disease-free equilibrium is globally asymptotically stable when Ro ≤ 1. It is also shown that this equilibrium is unstable when Ro > 1 and there exists a globally asymptotically stable endemic equilibr...

We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals move between populations according to a Markov transition matrix Σ and infectives can only make infectious contacts with members of their current population. Expressions for the basic reproduction number, R₀, and the probability of extinction of the epidemic are derived. It is shown t...

From March to July 1996 a measles outbreak occurred in northern Luxembourg with 110 reported cases centered around two primary schools (85 cases) and the surrounding community (25 cases). Eighty four suspected cases were confirmed serologically. Vaccine coverage was estimated from questionnaire-based surveys at the two primary schools to be 70 and 76%, respectively. Vaccine efficacy during the ...