Statistical Models in Engineering

Mosquito-borne Diseases

Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease

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Mathematical models of malaria - a review

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.

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

Background. During the influenza A(H1N1) pandemic, antiviral prescribing was limited, vaccines were not available early, and the effectiveness of nonpharmaceutical interventions (NPIs) was uncertain. Our study examined whether use of face masks and hand hygiene reduced the incidence of influenza-like illness (ILI). Methods. A randomized intervention trial involving 1437 young adults living in university residence halls during the 2006‐2007 influenza season was designed. Residence halls were randomly assigned to 1 of 3 groups— face mask use, face masks with hand hygiene, or control— for 6 weeks. Generalized models estimated rate ratios for clinically diagnosed or survey-reported ILI weekly and cumulatively. Results. We observed significant reductions in ILI during weeks 4‐6 in the mask and hand hygiene group, compared with the control group, ranging from 35% (confidence interval [CI], 9%‐53%) to 51% (CI, 13%‐73%), after adjusting for vaccination and other covariates. Face mask use alone showed a similar reduction in ILI compared with the control group, but adjusted estimates were not statistically significant. Neither face mask use and hand hygiene nor face mask use alone was associated with a significant reduction in the rate of ILI cumulatively. Conclusions. These findings suggest that face masks and hand hygiene may reduce respiratory illnesses in shared living settings and mitigate the impact of the influenza A(H1N1) pandemic. Trial Registration. ClinicalTrials.gov identifier: NCT00490633.

Mask use, hand hygiene, and seasonal influenza-like illness among young adults: A randomized intervention trial

Optimal control strategy of malaria vector using genetically modified mosquitoes.

Simulating malaria model for different treatment intensities in a variable environment

Two modern theories of biological evolution, one by Carl Woese, and the other by Lynn Margulis, are modelled with Volterra–Hamilton systems. Their predictions are evaluated and compared within this modelling framework. For example, Woese’s theory turns out to su8er from instability in its chemical exchanges processes, whereas Margulis’ does not. An introduction to the mathematical and biological ideas is included. ? 2003 Elsevier Science Ltd. All rights reserved.

Theories and models in symbiogenesis

Finite deformations of homogeneous, isotropic, incompressible initially flat, unstressed annular membranes under axisymmetric axial force and moment loads are studied. The general equilibrium equations and boundary conditions were established through the principle of stationary potential energy and the coupled, non-linear differential equations solved numerically, to obtain the angle of twist, the deflection and the radial deformation at every point of the membrane. Two strain energy densities are considered: neo-Hookean, for which it is possible to obtain a closed approximated solution, and Mooney-Rivlin. The results are prese'nted in non-dimensional form.

Large deformations under axial force and moment loads of initially flat annular membranes

The ultimate purpose of this paper is to present a new analytical formulation to simulate diffusion with retention in a reactive medium under stable thermodynamic conditions. The analysis of diffusion with retention in a continuum medium is developed after the solution of an equivalent problem using a discrete approach. The new law may be interpreted as the reduction of all diffusion processes with retention to a unifying phenomenon that can adequately simulate the retention effect namely a circulatory motion. It is remarkable that the governing equation requires a fourth order differential term as suggested by the discrete approach. The relative fraction of diffusion particles β is introduced as a control parameter in the diffusion-retention law as suggested by the discrete approach. This control parameter is essential to avoid retention isolated from the diffusion process. Two matrices referring to material properties are introduced and related to the real phenomenon through the circulation hypothesis. The governing equation may be highly non-linear even if the material properties are constant, but the retention effect is a function of the concentration level, that is, β is a function of the concentration.

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Luiz Bevilacqua

Papers

Optimal control strategy of malaria vector using genetically modified mosquitoes.

Simulating malaria model for different treatment intensities in a variable environment

Theories and models in symbiogenesis

Large deformations under axial force and moment loads of initially flat annular membranes

A new analytical formulation of retention effects on particle diffusion processes