Dengue is one of the major international public health concerns. Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. A model for the transmission of Dengue disease is presented. It consists of eight mutually exclusive compartments representing the human and vector dynamics. It also includes a con...

A  tuberculosis (TB) model with  lost sight  and multiple latent classes  is considered and studied. We derive the basic reproduction ratio $mathcal R_0$. There is always a globally asymptotically stable equilibrium state. Depending on the value of   $mathcal{R}_0$, this state can be either endemic ($mathcal{R}_0> 1$), or infection-free ($mathcal{R}_0leq 1$). The global asymptotic stability of ...

We consider a mathematical model that describes the interactions of the HIV virus, CD4 cells and CTLs within host, which is a modification of some existing models by incorporating (i) two distributed kernels reflecting the variance of time for virus to invade into cells and the variance of time for invaded virions to reproduce within cells; (ii) a nonlinear incidence function f for virus infect...

In this study, asymptotic analysis of an HIV-1 epidemic model with distributed intracellular delays is proposed. One delay term represents the latent period which is the time when the target cells are contacted by the virus particles and the time the contacted cells become actively infected and the second delay term represents the virus production period which is the time when the new virions a...

We present a model of a control programme for a disease outbreak in a population of livestock holdings. Control is achieved by culling infectious holdings when they are discovered and by the pre-emptive culling of livestock on holdings deemed to be at enhanced risk of infection. Because the pre-emptive control programme cannot directly identify exposed holdings, its implementation will result i...

We incorporate parameter heterogeneity in a two-patch susceptible-infectious-susceptible (SIS) epidemic model with infection during transport and prove that the disease-free and endemic equilibria are globally asymptotically stable when the basic reproduction number [Formula: see text] and [Formula: see text], respectively. We find that infection during transport increases the possibility that ...

The epidemiology of tularemia has influenced, perhaps incorrectly skewed, our views on the ecology of the agent of tularemia. In particular, the central role of lagomorphs needs to be reexamined. Diverse observations, some incidental, and some that are more generally reproducible, have not been synthesized so that the critical elements of the perpetuation of Francisella tularensis can be identi...

We are concerned with an epidemic in a closed population under the assumption that the per capita number of contacts remains constant, when population size diminishes due to the fatal consequences of the disease. We focus on the nal size as a function of the basic reproduction ratio R0 (which now is independent of population size!) and the survival probability f. Mathematically the model is des...