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      QUALITATIVE ASSESSMENT OF THE ROLE OF TEMPERATURE VARIATIONS ON MALARIA TRANSMISSION DYNAMICS

      1 , 2 , 3
      Journal of Biological Systems
      World Scientific Pub Co Pte Ltd

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          Abstract

          A new mechanistic deterministic model for assessing the impact of temperature variability on malaria transmission dynamics is developed. Sensitivity and uncertainty analyses of the model parameters reveal that, for temperature values in the range 16–[Formula: see text]C, the three parameters with the greatest influence on disease dynamics are the mosquito carrying capacity, transmission probability per contact for susceptible mosquitoes and human recruitment rate. This study emphasizes the combined use of mosquito-reduction strategies and personal protection against mosquito bites during periods when the mean monthly temperatures are in the range 16.7–25[Formula: see text]C. For higher monthly mean temperatures in the range 26–34[Formula: see text]C, mosquito-reduction strategies should be emphasized ahead of personal protection. Numerical simulations of the model reveal that mosquito maturation rate has a minimum sensitivity (to the associated reproduction threshold of the model) at 24[Formula: see text]C and maximum at 30[Formula: see text]C. The mosquito biting rate has maximum sensitivity at 26[Formula: see text]C, while the minimum value for the transmission probability per bite for susceptible mosquitoes occurs at 24[Formula: see text]C. Furthermore, it is shown, using mean monthly temperature data from 67 cities across the four regions of sub-Saharan Africa, that malaria burden (measured in terms of the total number of new cases of infection) increases with increasing temperature in the range 16–28[Formula: see text]C and decreases for temperature values above 28[Formula: see text]C in West Africa, 27[Formula: see text]C in Central Africa, 26[Formula: see text]C in East Africa and 25[Formula: see text]C in South Africa. These findings, which support and complement a recent study by other authors, reinforce the potential importance of temperature and temperature variability on future malaria transmission trends. Further simulations show that mechanistic malaria transmission models that do not incorporate temperature variability may under-estimate disease burden for temperature values in the range 23–27[Formula: see text]C, and over-estimate disease burden for temperature values in the ranges 16–22[Formula: see text]C and 28–32[Formula: see text]C. Additionally, models that do not explicitly incorporate the dynamics of immature mosquitoes may under- or over-estimate malaria burden, depending on mosquito abundance and mean monthly temperature profile in the community.

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          A methodology for performing global uncertainty and sensitivity analysis in systems biology.

          Accuracy of results from mathematical and computer models of biological systems is often complicated by the presence of uncertainties in experimental data that are used to estimate parameter values. Current mathematical modeling approaches typically use either single-parameter or local sensitivity analyses. However, these methods do not accurately assess uncertainty and sensitivity in the system as, by default, they hold all other parameters fixed at baseline values. Using techniques described within we demonstrate how a multi-dimensional parameter space can be studied globally so all uncertainties can be identified. Further, uncertainty and sensitivity analysis techniques can help to identify and ultimately control uncertainties. In this work we develop methods for applying existing analytical tools to perform analyses on a variety of mathematical and computer models. We compare two specific types of global sensitivity analysis indexes that have proven to be among the most robust and efficient. Through familiar and new examples of mathematical and computer models, we provide a complete methodology for performing these analyses, in both deterministic and stochastic settings, and propose novel techniques to handle problems encountered during these types of analyses.
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            Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission

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              On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations.

              The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.
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                Author and article information

                Journal
                Journal of Biological Systems
                J. Biol. Syst.
                World Scientific Pub Co Pte Ltd
                0218-3390
                1793-6470
                November 30 2015
                December 2015
                November 30 2015
                December 2015
                : 23
                : 04
                : 1550030
                Affiliations
                [1 ]Department of Ecology and Evolutionary Biology University of Kansas, Lawrence, KS 66045, USA
                [2 ]School of Mathematical and Statistical Sciences Arizona State University Tempe, Arizona 85287-1804, USA
                [3 ]Department of Public Health and Policy Faculty of Health and Life Sciences University of Liverpool Liverpool L69 3GL, UK
                Article
                10.1142/S0218339015500308
                9b8e10e1-1f40-4053-987a-f9740f696b86
                © 2015
                History

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