We formulate a deterministic model with two latent periods in the non-constant host and vector populations, in order to theoretically assess the potential impact of personal protection, treatment and possible vaccination strategies on the transmission dynamics of malaria. The thresholds and equilibria for the model are determined. The model is analysed… (More)
BACKGROUND There is an urgent need to understand how the provision of information influences individual risk perception and how this in turn shapes the evolution of epidemics. Individuals are influenced by information in complex and unpredictable ways. Emerging infectious diseases, such as the recent swine flu epidemic, may be particular hotspots for a… (More)
Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. We formulate a mathematical model that captures some essential dynamics of cholera transmission to study the impact of public health educational campaigns, vaccination and treatment as control… (More)
The widespread impact of avian influenza viruses not only poses risks to birds, but also to humans. The viruses spread from birds to humans and from human to human In addition, mutation in the primary strain will increase the infectiousness of avian influenza. We developed a mathematical model of avian influenza for both bird and human populations. The… (More)
A mathematical model was designed to explore the co-interaction of gonorrhea and HIV in the presence of antiretroviral therapy and gonorrhea treatment. Qualitative and comprehensive mathematical techniques have been used to analyse the model. The gonorrhea-only and HIV-only sub-models are first considered. Analytic expressions for the threshold parameter in… (More)
Dynamical systems, differential equations, difference equations, nonstandard finite difference schemes, mathematical epidemiology, and mathematical ecology.
We propose a method for partially discretizing a model of an age-dependent population dynamics with an additional structure whose growth rate is age-dependent. We give theoretical conditions under which a second order accuracy arises. A priori estimates are obtained. The main result indicates that the sum of these errors converges and is of second order… (More)