Based on the classical Ross-Macdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. The temporal heterogeneity is described by assuming that some model coefficients are time-periodic, while the spatial heterogeneity is modeled by using a multi-patch structure and assuming that individuals travel...

We propose a new threshold quantity for the analysis of the epidemiology of infectious diseases. The quantity is similar in concept to the familiar basic reproduction ratio, R0, but it singles out particular host types instead of providing a criterion that is uniform for all host types. Using this methodology we are able to identify the long-term effects of disease-control strategies for partic...

We provide a global analysis of systems of within-host parasitic infections. The systems studied have parallel classes of different length of latently infected target cells. These systems can also be thought as systems arising from within-host parasitic systems with distributed continuous delays. We compute the basic reproduction ratio R0 for the systems under consideration. If R0< or =1 the pa...

Salmonella is a cause of concern in the cattle industry, because it is a zoonosis causing severe invasive infections in humans and because it causes economic and welfare losses in infected herds. In general, cattle in the Netherlands are infected with two types; Salmonella Dublin and Salmonella Typhimurium. Both types cause clinical signs but S. Dublin outbreaks are more prevalent and clinical ...

An SEI metapopulation model is developed for the spread of an infectious agent by migration. The model portrays two age classes on a number of patches connected by migration routes which are used as host animals mature. A feature of this model is that the basic reproduction ratio may be computed directly, using a scheme that separates topography, demography, and epidemiology. We also provide fo...

We developed a method to produce time-varying maps for dengue transmission risk, using the Ross-Macdonald framework and differential equations estimate spatially basic reproduction number (R0) of vector-borne disease. The components R0 formula were derived partly from mosquito population dynamics model integrating meteorological environmental variables, temperature-dependent functions vector co...

This study presents an improved mathematical model for Hepatitis B Virus (HBV) transmission dynamics by investigating autonomous and nonautonomous cases. The novel incorporates the effects of medical treatment, allowing a more comprehensive understanding HBV potential control measures. Our analysis involves verifying unique solutions’ existence, ensuring positivity over time, conducting stabili...

The basic reproduction number, R0 is a measure of the potential for disease spread in a population. Mathematically, R0 is a threshold for stability of a disease-free equilibrium and is related to the peak and final size of an epidemic. The purpose of these notes is to give a precise definition and algorithm for obtaining R0 for a general compartmental ordinary differential equation model of dis...

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...