A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010

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.

Recasting the theory of mosquito-borne pathogen transmission dynamics and control

Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of theworld. 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 nowused 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 formosquito blood feeding, themovement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.

Raman and infrared spectroscopic characterization of the phosphate mineral Lithiophilite—LiMnPO4

The metal lithium is very important in industry, including lithium batteries. An important source of lithium besides continental brines is granitic pegmatites as in Australia. Lithiophilite is a lithium and manganese phosphate with chemical formula LiMnPO4 and forms a solid solution with triphylite, its Fe analog, and belongs to the triphylite group that includes karenwebberite, natrophilite, and sicklerite. The mineral lithiophilite was characterized by chemical analysis and spectroscopic techniques. The chemical is: Li1.01(Mn0.60, Fe0.41, Mg0.01, Ca0.01)(PO4)0.99 and corresponds to an intermediate member of the triphylite-lithiophilite series, with predominance of the lithiophilite member. The mineral lithiophilite is readily characterized by Raman and infrared spectroscopy.