Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.

Cholera is an ancient disease that continues to cause epidemic and pandemic disease despite ongoing efforts to limit its spread. Mathematical models provide one means of assessing the utility of various proposed interventions. However, cholera models that have been developed to date have had limitations, suggesting that there are basic elements of cholera transmission that we still do not understand. Recent laboratory findings suggest that passage of Vibrio cholerae O1 Inaba El Tor through the gastrointestinal tract results in a short-lived, hyperinfectious state of the organism that decays in a matter of hours into a state of lower infectiousness. Incorporation of this hyperinfectious state into our disease model provides a much better fit with the observed epidemic pattern of cholera. These findings help to substantiate the clinical relevance of laboratory observations regarding the hyperinfectious state, and underscore the critical importance of human-to-human versus environment-to-human transmission in the generation of epidemic and pandemic disease. To have maximal impact on limiting epidemic spread of cholera, interventions should be targeted toward minimizing risk of transmission of the short-lived, hyperinfectious form of toxigenic Vibrio cholerae. The possibility of comparable hyperinfectious states in other major epidemic diseases also needs to be evaluated and, as appropriate, incorporated into models of disease prevention.

Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of the world. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonald's formula for R₀ and its entomological derivative, vectorial capacity, are now used to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross–Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context for mosquito blood feeding, the movement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.

To facilitate rapid detection of a future bioterrorist attack, an increasing number of public health departments are investing in new surveillance systems that target the early manifestations of bioterrorism-related disease. Whether this approach is likely to detect an epidemic sooner than reporting by alert clinicians remains unknown. The detection of a bioterrorism-related epidemic will depend on population characteristics, availability and use of health services, the nature of an attack, epidemiologic features of individual diseases, surveillance methods, and the capacity of health departments to respond to alerts. Predicting how these factors will combine in a bioterrorism attack may be impossible. Nevertheless, understanding their likely effect on epidemic detection should help define the usefulness of syndromic surveillance and identify approaches to increasing the likelihood that clinicians recognize and report an epidemic.

A model is formulated that describes the spatial propagation of a disease that can be transmitted between multiple species. The spatial component consists, for each species, of a certain number of patches that make up the vertices of a digraph, the arcs of which represent the movement of the various species between the patches. In each of the patches and for each species, a susceptible-exposed-infectious-recovered (SEIR) epidemic model describes the evolution of the disease status of individuals. Also in each patch, there is transmission of the disease from species to species. An analysis of the system is given, beginning with results on the mobility component. A formula is derived for the computation of the basic reproduction number R₀ for sspecies and npatches, which then determines the global stability properties of the disease free equilibrium. Simulations for the spread of a disease in one species and two patches are presented.