A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications

[EN] This paper provides a comprehensive probabilistic analysis of a full randomization of approximate SIR-type epidemiological models based on discrete-time Markov chain formulation. The randomization is performed by assuming that all input data (initial conditions, the contagion, and recovering rates involved in the transition matrix) are random variables instead of deterministic constants. In the first part of the paper, we determine explicit expressions for the so called first probability density function of each subpopulation identified as the corresponding states of the Markov chain (susceptible, infected, and recovered) in terms of the probability density function of each input random variable. Afterwards, we obtain the probability density functions of the times until a given proportion of the population remains susceptible, infected, and recovered, respectively. The theoretical analysis is completed by computing explicit expressions of important randomized epidemiological quantities, namely, the basic reproduction number, the effective reproduction number, and the herd immunity threshold. The study is conducted under very general assumptions and taking extensive advantage of the random variable transformation technique. The second part of the paper is devoted to apply our theoretical findings to describe the dynamics of the pandemic influenza in Egypt using simulated data excerpted from the literature. The simulations are complemented with valuable information, which is seldom displayed in epidemiological models. In spite of the nonlinear mathematical nature of SIR epidemiological model, our results show a strong agreement with the approximation via an appropriate randomized Markov chain. A justification in this regard is discussed.Spanish Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-P; Generalitat Valenciana, Grant/Award Number: APOSTD/2019/128; Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-PCortés, J.; El-Labany, S.; Navarro-Quiles, A.; Selim, MM.; Slama, H. (2020). A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications. Mathematical Methods in the Applied Sciences. 43(14):8204-8222. https://doi.org/10.1002/mma.6482S820482224314Hamra, G., MacLehose, R., & Richardson, D. (2013). Markov Chain Monte Carlo: an introduction for epidemiologists. International Journal of Epidemiology, 42(2), 627-634. doi:10.1093/ije/dyt043Becker, N. (1981). A General Chain Binomial Model for Infectious Diseases. Biometrics, 37(2), 251. doi:10.2307/2530415Allen, L. J. S. (2010). An Introduction to Stochastic Processes with Applications to Biology. doi:10.1201/b12537Hethcote, H. W. (2000). The Mathematics of Infectious Diseases. SIAM Review, 42(4), 599-653. doi:10.1137/s0036144500371907Brauer, F., & Castillo-Chávez, C. (2001). Mathematical Models in Population Biology and Epidemiology. Texts in Applied Mathematics. doi:10.1007/978-1-4757-3516-1Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2018). Some results about randomized binary Markov chains: theory, computing and applications. International Journal of Computer Mathematics, 97(1-2), 141-156. doi:10.1080/00207160.2018.1440290Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2017). Randomizing the parameters of a Markov chain to model the stroke disease: A technical generalization of established computational methodologies towards improving real applications. Journal of Computational and Applied Mathematics, 324, 225-240. doi:10.1016/j.cam.2017.04.040Casabán, M.-C., Cortés, J.-C., Romero, J.-V., & Roselló, M.-D. (2015). Probabilistic solution of random SI-type epidemiological models using the Random Variable Transformation technique. Communications in Nonlinear Science and Numerical Simulation, 24(1-3), 86-97. doi:10.1016/j.cnsns.2014.12.016Casabán, M.-C., Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., Roselló, M.-D., & Villanueva, R.-J. (2016). A comprehensive probabilistic solution of random SIS-type epidemiological models using the random variable transformation technique. Communications in Nonlinear Science and Numerical Simulation, 32, 199-210. doi:10.1016/j.cnsns.2015.08.009Slama, H., Hussein, A., El-Bedwhey, N. A., & Selim, M. M. (2019). An approximate probabilistic solution of a random SIR-type epidemiological model using RVT technique. Applied Mathematics and Computation, 361, 144-156. doi:10.1016/j.amc.2019.05.019Slama, H., El-Bedwhey, N. A., El-Depsy, A., & Selim, M. M. (2017). Solution of the finite Milne problem in stochastic media with RVT Technique. The European Physical Journal Plus, 132(12). doi:10.1140/epjp/i2017-11763-6Kegan, B., & West, R. W. (2005). Modeling the simple epidemic with deterministic differential equations and random initial conditions. Mathematical Biosciences, 195(2), 179-193. doi:10.1016/j.mbs.2005.02.004Dorini, F. A., Cecconello, M. S., & Dorini, L. B. (2016). On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Communications in Nonlinear Science and Numerical Simulation, 33, 160-173. doi:10.1016/j.cnsns.2015.09.009Van den Driessche, P. (2017). Reproduction numbers of infectious disease models. Infectious Disease Modelling, 2(3), 288-303. doi:10.1016/j.idm.2017.06.002Heffernan, J. ., Smith, R. ., & Wahl, L. . (2005). Perspectives on the basic reproductive ratio. Journal of The Royal Society Interface, 2(4), 281-293. doi:10.1098/rsif.2005.0042Khalil, K. M., Abdel-Aziz, M., Nazmy, T. T., & Salem, A.-B. M. (2012). An Agent-Based Modeling for Pandemic Influenza in Egypt. Intelligent Systems Reference Library, 205-218. doi:10.1007/978-3-642-25755-1_1

Landscape of stimulation-responsive chromatin across diverse human immune cells.

A hallmark of the immune system is the interplay among specialized cell types transitioning between resting and stimulated states. The gene regulatory landscape of this dynamic system has not been fully characterized in human cells. Here we collected assay for transposase-accessible chromatin using sequencing (ATAC-seq) and RNA sequencing data under resting and stimulated conditions for up to 32 immune cell populations. Stimulation caused widespread chromatin remodeling, including response elements shared between stimulated B and T cells. Furthermore, several autoimmune traits showed significant heritability in stimulation-responsive elements from distinct cell types, highlighting the importance of these cell states in autoimmunity. Allele-specific read mapping identified variants that alter chromatin accessibility in particular conditions, allowing us to observe evidence of function for a candidate causal variant that is undetected by existing large-scale studies in resting cells. Our results provide a resource of chromatin dynamics and highlight the need to characterize the effects of genetic variation in stimulated cells

Building Babies - Chapter 16

In contrast to birds, male mammals rarely help to raise the offspring. Of all mammals, only among rodents, carnivores, and primates, males are sometimes intensively engaged in providing infant care (Kleiman and Malcolm 1981). Male caretaking of infants has long been recognized in nonhuman primates (Itani 1959). Given that infant care behavior can have a positive effect on the infant’s development, growth, well-being, or survival, why are male mammals not more frequently involved in “building babies”? We begin the chapter defining a few relevant terms and introducing the theory and hypotheses that have historically addressed the evolution of paternal care. We then review empirical findings on male care among primate taxa, before focusing, in the final section, on our own work on paternal care in South American owl monkeys (Aotus spp.). We conclude the chapter with some suggestions for future studies.Deutsche Forschungsgemeinschaft (HU 1746/2-1) Wenner-Gren Foundation, the L.S.B. Leakey Foundation, the National Geographic Society, the National Science Foundation (BCS-0621020), the University of Pennsylvania Research Foundation, the Zoological Society of San Dieg

Nanoparticles in cigarette smoke; real-time undiluted measurements by a scanning mobility particle sizer

Cigarette smoke is a complex mixture of smoke constituents, often characterised by size-resolved particle distributions. Since descriptions of ultrafine particles <50 nm are absent, our aim was to explore the existence of these nanoparticles in fresh and undiluted cigarette smoke. We measured undiluted smoke particles real-time by a scanning mobility particle sizer with Faraday cup electrometer, integrated in our custom-made smoking machine. Cigarettes were smoked by 2 s puffs, 30 s puff intervals and 50 ml puff volume. We tested six different cigarettes (1–10 mg tar per cigarette) at ten particle size-ranges between 6 and 50 nm, and repeated measurements five times. The formation of nanoparticles in fresh cigarette smoke was observed over the entire range between 6 and 50 nm, and reproduced in all cigarettes. The highest mean yield was 8.8 × 109 (SD = 1.1 × 109) particles per cigarette at the largest particle size range by high-tar cigarettes. Nanoparticle counts appear to increase with particle size, claimed tar values and blocking of filter ventilation holes, and inversely with butt length. Fresh undiluted cigarette smoke contains large amounts of potentially toxic nanoparticles <50 nm. We recommend to further study nanoparticles in the characterisation of cigarette smoke

A cross-national study on the antecedents of work–life balance from the fit and balance perspective

Drawing on the perceived work–family fit and balance perspective, this study investigates demands and resources as antecedents of work–life balance (WLB) across four countries (New Zealand, France, Italy and Spain), so as to provide empirical cross-national evidence. Using structural equation modelling analysis on a sample of 870 full time employees, we found that work demands, hours worked and family demands were negatively related to WLB, while job autonomy and supervisor support were positively related to WLB. We also found evidence that resources (job autonomy and supervisor support) moderated the relationships between demands and work–life balance, with high resources consistently buffering any detrimental influence of demands on WLB. Furthermore, our study identified additional predictors of WLB that were unique to some national contexts. For example, in France and Italy, overtime hours worked were negatively associated with WLB, while parental status was positively associated with WLB. Overall, the implications for theory and practice are discussed.Peer ReviewedPostprint (author's final draft

Prevalence of coronary artery disease risk factors in Iran: a population based survey

<p>Abstract</p> <p>Background</p> <p>Coronary artery disease (CAD) is a leading cause of mortality, morbidity, and disability with high health care cost in Iran. It accounts for nearly 50 percent of all deaths per year. Yet little is known about CAD and CAD risk factors in the Iranian population. We aimed to assess the prevalence of different CAD risk factors in an Iranian population.</p> <p>Methods</p> <p>A descriptive cross sectional survey was conducted involving 3000 healthy adults at 18 years of age or above who were recruited with cluster random sampling. Demographic data and risk factors were determined by taking history, physical examination and laboratory tests.</p> <p>Results</p> <p>The average age was 36.23 ± 15.26. There was 1381 female (46%) and 1619 male (54%) out of which 6.3% were diabetic, 21.6% were smoker, and 15% had positive familial heart disease history. 61% had total cholesterol level > 200 mg/dL, 32% triglyceride > 200 mg/dl, 47.5% LDL-c > 130 mg/dl, 5.4% HDL-c < 35 mg/dl, 13.7% systolic blood pressure > 140 mmHg, 9.1% diastolic blood pressure > 90 mmHg and 87% of them were physically inactive.</p> <p>Conclusion</p> <p>Clinical and Para-clinical data indicated that Iranian adult population are of a high level of CAD risk factors, which may require urgent decision making to address national control measures regarding CAD.</p

Relation between body mass index and depression: a structural equation modeling approach

<p>Abstract</p> <p>Background</p> <p>Obesity and depression are two major diseases which are associated with many other health problems such as hypertension, dyslipidemia, diabetes mellitus, coronary heart disease, stroke, myocardial infarction, heart failure in patients with systolic hypertension, low bone mineral density and increased mortality. Both diseases share common health complications but there are inconsistent findings concerning the relationship between obesity and depression. In this work we used the <it>structural equation modeling </it>(SEM) technique to examine the relation between body mass index (BMI), as a proxy for obesity, and depression using the Canadian Community Health Survey, Cycle 1.2.</p> <p>Methods</p> <p>In this SEM model we postulate that 1) BMI and depression are directly related, 2) BMI is directly affected by the physical activity and, 3)depression is directly influenced by stress. SEM was also used to assess the relation between BMI and depression separately for males and females.</p> <p>Results</p> <p>The results indicate that higher BMI is associated with more severe form of depression. On the other hand, the more severe form of depression may result in less weight gain. However, the association between depression and BMI is gender dependent. In males, the higher BMI may result in a more severe form of depression while in females the relation may not be the same. Also, there was a negative relationship between physical activity and BMI.</p> <p>Conclusion</p> <p>In general, use of SEM method showed that the two major diseases, obesity and depression, are associated but the form of the relation is different among males and females. More research is necessary to further understand the complexity of the relationship between obesity and depression. It also demonstrated that SEM is a feasible technique for modeling the relation between obesity and depression.</p