A unified numerical model of collisional depolarization and broadening rates due to hydrogen atom collisions

Interpretation of solar polarization spectra accounting for partial or complete frequency redistribution requires data on various collisional processes. Data for depolarization and polarization transfer are needed but often missing, while data for collisional broadening are usually more readily available. Recent work by Sahal-Br\'echot and Bommier concluded that despite underlying similarities in the physics of collisional broadening and depolarization processes, relationships between them are not possible to derive purely analytically. We aim to derive accurate numerical relationships between the collisional broadening rates and the collisional depolarization and polarization transfer rates due to hydrogen atom collisions. Such relationships would enable accurate and efficient estimation of collisional data for solar applications. Using earlier results for broadening and depolarization processes based on general (i.e. not specific to a given atom), semi-classical calculations employing interaction potentials from perturbation theory, genetic programming (GP) has been used to fit the available data and generate analytical functions describing the relationships between them. The predicted relationships from the GP-based model are compared with the original data to estimate the accuracy of the method.Comment: 10 pages, 7 figures, Accepted for publication in Astronomy & Astrophysic

The Effect of Physical Exercise on the Dynamics of Glucose and Insulin

Abstract Regular physical activity is indicated either to prevent and delay the onset of non-insulin-dependent diabetes or to assure a good control of diabetes by increasing insulin sensitivity and ameliorating the metabolism of glucose disappearance. Many studies and experiments have dealt with this subject. In this paper, we introduce the effect of physical activity via parameters of a mathematical model which allows us to compare the behaviour of blood glucose in normal, non-insulin-dependent diabetes and insulin-dependent diabetes people, with and without physical effort. Extreme cases of physical activity leading to hypoglycaemia or aggravating hyperglycaemia are also underlined.

A model of dengue fever

BACKGROUND: Dengue is a disease which is now endemic in more than 100 countries of Africa, America, Asia and the Western Pacific. It is transmitted to the man by mosquitoes (Aedes) and exists in two forms: Dengue Fever and Dengue Haemorrhagic Fever. The disease can be contracted by one of the four different viruses. Moreover, immunity is acquired only to the serotype contracted and a contact with a second serotype becomes more dangerous. METHODS: The present paper deals with a succession of two epidemics caused by two different viruses. The dynamics of the disease is studied by a compartmental model involving ordinary differential equations for the human and the mosquito populations. RESULTS: Stability of the equilibrium points is given and a simulation is carried out with different values of the parameters. The epidemic dynamics is discussed and illustration is given by figures for different values of the parameters. CONCLUSION: The proposed model allows for better understanding of the disease dynamics. Environment and vaccination strategies are discussed especially in the case of the succession of two epidemics with two different viruses

A stage structured mosquito model incorporating effects of precipitation and daily temperature fluctuations

An outbreak of dengue fever in Guangdong province in 2014 was the most serious outbreak ever recorded in China. Given the known positive correlation between the abundance of mosquitoes and the number of dengue fever cases, a stagestructured mosquito model was developed to investigate the cause of the large abundance of mosquitoes in 2014 and its implications for outbreaks of the disease. Data on the Breteau index (number of containers positive for larvae per 100 premises investigated), temperature and precipitation were used for model fitting. The egg laying rate, the development rate and the mortality rates of immatures and adults were obtained from the estimated parameters. Moreover, effects of daily fluctuations of temperature on these parameters were obtained and the effects of temperature and precipitation were analyzed by simulations. Our results indicated that the abundance of mosquitoes depended not only on the total annual precipitation but also on the distribution of the precipitation. The daily mean temperature had a nonlinear relationship with the abundance of mosquitoes, and large diurnal temperature differences can reduce the abundance of mosquitoes. In addition, effects of increasing precipitation and temperature were interdependent. Our findings suggest that the large abundance of mosquitoes in 2014 was mainly caused by the distribution of the precipitation. In the perspective of mosquito control, our results reveal that it is better to clear water early and spray insecticide between April and August in case of limited resources

A mathematical model for the burden of diabetes and its complications

BACKGROUND: The incidence and prevalence of diabetes are increasing all over the world. Complications of diabetes constitute a burden for the individuals and the whole society. METHODS: In the present paper, ordinary differential equations and numerical approximations are used to monitor the size of populations of diabetes with and without complications. RESULTS: Different scenarios are discussed according to a set of parameters and the dynamical evolution of the population from the stage of diabetes to the stage of diabetes with complications is clearly illustrated. CONCLUSIONS: The model shows how efficient and cost-effective strategies can be obtained by acting on diabetes incidence and/or controlling the evolution to the stage of complications

Modelling the regulatory system for diabetes mellitus with a threshold window

Piecewise (or non-smooth) glucose-insulin models with threshold windows for type 1 and type 2 diabetes mellitus are proposed and analyzed with a view to improving understanding of the glucose-insulin regulatory system. For glucose-insulin models with a single threshold, the existence and stability of regular, virtual, pseudo-equilibria and tangent points are addressed. Then the relations between regular equilibria and a pseudo-equilibrium are studied. Furthermore, the sufficient and necessary conditions for the global stability of regular equilibria and the pseudo-equilibrium are provided by using qualitative analysis techniques of non-smooth Filippov dynamic systems. Sliding bifurcations related to boundary node bifurcations were investigated with theoretical and numerical techniques, and insulin clinical therapies are discussed. For glucose-insulin models with a threshold window, the effects of glucose thresholds or the widths of threshold windows on the durations of insulin therapy and glucose infusion were addressed. The duration of the effects of an insulin injection is sensitive to the variation of thresholds. Our results indicate that blood glucose level can be maintained within a normal range using piecewise glucose-insulin models with a single threshold or a threshold window. Moreover, our findings suggest that it is critical to individualize insulin therapy for each patient separately, based on initial blood glucose levels

Small-scale solar magnetic fields

As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research.Comment: 43 pages, 18 figure

Seroprevalence of Toxoplasma gondii infection in arthritis patients in eastern China

Background: There is accumulating evidence for an increased susceptibility to infection in patients with arthritis. We sought to understand the epidemiology of Toxoplasma gondii infection in arthritis patients in eastern China, given the paucity of data on the magnitude of T. gondii infection in these patients. Methods: Seroprevalence of T. gondii infection was assessed by enzyme-linked immunosorbent assay using a crude antigen of the parasite in 820 arthritic patients, and an equal number of healthy controls, from Qingdao and Weihai cities, eastern China. Sociodemographic, clinical and lifestyle information on the study participants were also obtained. Results: The prevalence of anti-T. gondii IgG was significantly higher in arthritic patients (18.8%) compared with 12% in healthy controls (P < 0.001). Twelve patients with arthritis had anti-T. gondii IgM antibodies comparable with 10 control patients (1.5% vs 1.2%). Demographic factors did not significantly influence these seroprevalence frequencies. The highest T. gondii infection seropositivity rate was detected in patients with rheumatoid arthritis (24.8%), followed by reactive arthritis (23.8%), osteoarthritis (19%), infectious arthritis (18.4%) and gouty arthritis (14.8%). Seroprevalence rates of rheumatoid arthritis and reactive arthritis were significantly higher when compared with controls (P < 0.001 and P = 0.002, respectively). A significant association was detected between T. gondii infection and cats being present in the home in arthritic patients (odds ratio [OR], 1.68; 95% confidence interval [CI]: 1.24 – 2.28; P = 0.001). Conclusions: These findings are consistent with and extend previous results, providing further evidence to support a link between contact with cats and an increased risk of T. gondii infection. Our study is also the first to confirm an association between T. gondii infection and arthritis patients in China. Implications for better prevention and control of T. gondii infection in arthritis patients are discussed. Trial registration: This is an epidemiological survey, therefore trial registration was not required

Smart Sensors and Virtual Physiology Human Approach as a Basis of Personalized Therapies in Diabetes Mellitus

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient’s information to the models

A critical review of mathematical models and data used in diabetology

The literature dealing with mathematical modelling for diabetes is abundant. During the last decades, a variety of models have been devoted to different aspects of diabetes, including glucose and insulin dynamics, management and complications prevention, cost and cost-effectiveness of strategies and epidemiology of diabetes in general. Several reviews are published regularly on mathematical models used for specific aspects of diabetes. In the present paper we propose a global overview of mathematical models dealing with many aspects of diabetes and using various tools. The review includes, side by side, models which are simple and/or comprehensive; deterministic and/or stochastic; continuous and/or discrete; using ordinary differential equations, partial differential equations, optimal control theory, integral equations, matrix analysis and computer algorithms