Mathematical Model
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2021 ◽  
Vol 18 (1) ◽  
Marcos Amaku ◽  
Dimas Tadeu Covas ◽  
Francisco Antonio Bezerra Coutinho ◽  
Raymundo Soares Azevedo ◽  
Eduardo Massad

Abstract Background At the moment we have more than 177 million cases and 3.8 million deaths (as of June 2021) around the world and vaccination represents the only hope to control the pandemic. Imperfections in planning vaccine acquisition and difficulties in implementing distribution among the population, however, have hampered the control of the virus so far. Methods We propose a new mathematical model to estimate the impact of vaccination delay against the 2019 coronavirus disease (COVID-19) on the number of cases and deaths due to the disease in Brazil. We apply the model to Brazil as a whole and to the State of Sao Paulo, the most affected by COVID-19 in Brazil. We simulated the model for the populations of the State of Sao Paulo and Brazil as a whole, varying the scenarios related to vaccine efficacy and compliance from the populations. Results The model projects that, in the absence of vaccination, almost 170 thousand deaths and more than 350 thousand deaths will occur by the end of 2021 for Sao Paulo and Brazil, respectively. If in contrast, Sao Paulo and Brazil had enough vaccine supply and so started a vaccination campaign in January with the maximum vaccination rate, compliance and efficacy, they could have averted more than 112 thousand deaths and 127 thousand deaths, respectively. In addition, for each month of delay the number of deaths increases monotonically in a logarithmic fashion, for both the State of Sao Paulo and Brazil as a whole. Conclusions Our model shows that the current delay in the vaccination schedules that is observed in many countries has serious consequences in terms of mortality by the disease and should serve as an alert to health authorities to speed the process up such that the highest number of people to be immunized is reached in the shortest period of time.

2021 ◽  
Vol 11 (1) ◽  
Xingyu Li ◽  
Amin Ghadami ◽  
John M. Drake ◽  
Pejman Rohani ◽  
Bogdan I. Epureanu

AbstractThe pandemic of COVID-19 has become one of the greatest threats to human health, causing severe disruptions in the global supply chain, and compromising health care delivery worldwide. Although government authorities sought to contain the spread of SARS-CoV-2, by restricting travel and in-person activities, failure to deploy time-sensitive strategies in ramping-up of critical resource production exacerbated the outbreak. Here, we developed a mathematical model to analyze the effects of the interaction between supply chain disruption and infectious disease dynamics using coupled production and disease networks built on global data. Analysis of the supply chain model suggests that time-sensitive containment strategies could be created to balance objectives in pandemic control and economic losses, leading to a spatiotemporal separation of infection peaks that alleviates the societal impact of the disease. A lean resource allocation strategy can reduce the impact of supply chain shortages from 11.91 to 1.11% in North America. Our model highlights the importance of cross-sectoral coordination and region-wise collaboration to optimally contain a pandemic and provides a framework that could advance the containment and model-based decision making for future pandemics.

2021 ◽  
Vol 11 (1) ◽  
V. R. Sanal Kumar ◽  
Vigneshwaran Sankar ◽  
Nichith Chandrasekaran ◽  
Sulthan Ariff Rahman Mohamed Rafic ◽  
Ajith Sukumaran ◽  

AbstractEvidences are escalating on the diverse neurological-disorders and asymptomatic cardiovascular-diseases associated with COVID-19 pandemic due to the Sanal-flow-choking. Herein, we established the proof of the concept of nanoscale Sanal-flow-choking in real-world fluid-flow systems using a closed-form-analytical-model. This mathematical-model is capable of predicting exactly the 3D-boundary-layer-blockage factor of nanoscale diabatic-fluid-flow systems (flow involves the transfer of heat) at the Sanal-flow-choking condition. As the pressure of the diabatic nanofluid and/or non-continuum-flows rises, average-mean-free-path diminishes and thus, the Knudsen-number lowers heading to a zero-slip wall-boundary condition with the compressible-viscous-flow regime in the nanoscale-tubes leading to Sanal-flow-choking due to the sonic-fluid-throat effect. At the Sanal-flow-choking condition the total-to-static pressure ratio (ie., systolic-to-diastolic pressure ratio) is a unique function of the heat-capacity-ratio of the real-world flows. The innovation of the nanoscale Sanal-flow-choking model is established herein through the entropy relation, as it satisfies all the conservation-laws of nature. The physical insight of the boundary-layer-blockage persuaded nanoscale Sanal-flow-choking in diabatic flows presented in this article sheds light on finding solutions to numerous unresolved scientific problems in physical, chemical and biological sciences carried forward over the centuries because the mathematical-model describing the phenomenon of Sanal-flow-choking is a unique scientific-language of the real-world-fluid flows. The 3D-boundary-layer-blockage factors presented herein for various gases are universal-benchmark-data for performing high-fidelity in silico, in vitro and in vivo experiments in nanotubes.

David Escors ◽  
Grazyna Kochan

General relativity is a theory for gravitation based on Riemannian geometry, difficult to compatibilize with quantum mechanics. This is evident in relativistic problems in which quantum effects cannot be discarded. For example in quantum gravity, gravitation of zero-point energy or events close to a black hole singularity. Here, we set up a mathematical model to select general relativity geodesics according to compatibility with the uncertainty principle. To achieve this, we derived a geometric expression of the uncertainty principle (GUP). This formulation identified proper space-time length with Planck length by a geodesic-derived scalar. GUP imposed a minimum allowed value for the interval of proper space-time which depended on the particular space-time geometry. GUP forced the introduction of a “zero-point” curvature perturbation over flat Minkowski space, caused exclusively by quantum uncertainty but not to gravitation. When applied to the Schwarzschild metric and choosing radial-dependent geodesics, our mathematical model identified a particle exclusion zone close to the singularity, similar to calculations by loop quantum gravity. For a 2 black hole merger, this exclusion zone was shown to have a radius that cannot go below a value proportional to the energy/mass of the incoming black hole multiplied by Planck length.

2021 ◽  
Mikhail Basov ◽  
Denis Prigodskiy

Abstract A mathematical model of an ultrahigh sensitivity piezoresistive chip of a pressure sensor with a range from -0.5 to 0.5 kPa has been developed. The optimum geometrical dimensions of a specific silicon membrane with a combination of rigid islands to ensure a trade-off relationship between sensitivity (Ssamples = 34.5 mV/kPa/V) and nonlinearity (2KNL samples = 0.81 %FS) have been determined. The paper also studies the range of the membrane deflection and makes recommendations on position of stops limiting diaphragm deflection in both directions; the stops allow for increasing burst pressure Pburst up to 450 кPa. The simulated data has been related to that of experimental samples and their comparative analysis showed the relevance of the mathematical model (estimated sensitivity and nonlinearity errors calculated on the basis of average values are 1.5% and 19%, respectively).

2021 ◽  
Timothy A. McLennan-Smith ◽  
Alexander C. Kalloniatis ◽  
Zlatko Jovanoski ◽  
Harvinder S. Sidhu ◽  
Dale O. Roberts ◽  

Tools from mathematical ecology in a combat model with humanitarian aid agencies Conflict models have a long history of taking inspiration from mathematical ecology. In “A mathematical model of humanitarian aid agencies in attritional conflict environments,” McLennan-Smith et al. seek to enrich counterinsurgency (COIN) warfare models to account for modern and future complexities by incorporating nontrophic effects and the functional response from mathematical ecology. The authors consider the application of these ideas in a COIN scenario in which a humanitarian aid agency is present in the conflict environment to support the local population. In this scenario, the aid agency plays the unwilling role of a “hospital shield” whereby it is forced to, or inadvertently, shield combatants or weapons. In contrast to the typical behavior seen in the classic Lanchester system, this model gives rise to limit cycles and bifurcations that the authors interpret through a warfighting application. Finally, through a case study, the authors highlight the importance of the agility of an intervention force in achieving victory when humanitarian aid agencies are present.

2021 ◽  
Vol 17 (7) ◽  
pp. e1009231
Leon Avery ◽  
Brian Ingalls ◽  
Catherine Dumur ◽  
Alexander Artyukhin

We describe a mathematical model for the aggregation of starved first-stage C elegans larvae (L1s). We propose that starved L1s produce and respond chemotactically to two labile diffusible chemical signals, a short-range attractant and a longer range repellent. This model takes the mathematical form of three coupled partial differential equations, one that describes the movement of the worms and one for each of the chemical signals. Numerical solution of these equations produced a pattern of aggregates that resembled that of worm aggregates observed in experiments. We also describe the identification of a sensory receptor gene, srh–2, whose expression is induced under conditions that promote L1 aggregation. Worms whose srh–2 gene has been knocked out form irregularly shaped aggregates. Our model suggests this phenotype may be explained by the mutant worms slowing their movement more quickly than the wild type.

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0253542
Andrew Marcus ◽  
Taylor L. Davis ◽  
Bruce E. Rittmann ◽  
John K. DiBaise ◽  
Elvis A. Carnero ◽  

Background The large intestine provides a compensatory role in energy recovery when surgical interventions such as extensive small intestinal resections or bypass operations lower the efficiency of nutrient absorption in the upper gastrointestinal (GI) tract. While microorganisms in the colon are known to play vital roles in recovering energy, their contributions remain to be qualified and quantified in the small intestine resection. Objective We develop a mathematical model that links nutrient absorption in the upper and lower GI tract in two steps. Methods First, we describe the effects of small intestine resection on the ileocecal output (ICO), which enters the colon and provides food for microbes. Second, we describe energy recovered by the colon’s microorganisms via short-chain fatty acid (SCFA) production. We obtain model parameters by performing a least-squares regression analysis on clinical data for subjects with normal physiology and those who had undergone small intestine resection. Results For subjects with their intestines intact, our model provided a metabolizable energy value that aligns well with the traditional Atwater coefficients. With removal of the small intestine, physiological absorption became less efficient, and the metabolizable energy decreased. In parallel, the inefficiencies in physiological absorption by the small intestine are partly compensated by production of short-chain fatty acids (SCFA) from proteins and carbohydrates by microorganisms in the colon. The colon recovered more than half of the gross energy intake when the entire small intestine was removed. Meanwhile, the quality of energy absorbed changed, because microbe-derived SCFAs, not the original components of food, become the dominant form of absorbed energy. Conclusion The mathematical model developed here provides an important framework for describing the effect of clinical interventions on the colon’s microorganisms.

James A. Hay ◽  
Joel Hellewell ◽  
Xueting Qiu

AbstractWidespread, repeated testing using rapid antigen tests to proactively detect asymptomatic SARS-CoV-2 infections has been a promising yet controversial topic during the COVID-19 pandemic. Concerns have been raised over whether currently authorized lateral flow tests are sufficiently sensitive and specific to detect enough infections to impact transmission whilst minimizing unnecessary isolation of false positives. These concerns have often been illustrated using simple, textbook calculations of positivity rates and positive predictive value assuming fixed values for sensitivity, specificity and prevalence. However, we argue that evaluating repeated testing strategies requires the consideration of three additional factors: new infections continue to arise depending on the incidence rate, isolating positive individuals reduces prevalence in the tested population, and each infected individual is tested multiple times during their infection course. We provide a simple mathematical model with an online interface to illustrate how these three factors impact test positivity rates and the number of isolating individuals over time. These results highlight the potential pitfalls of using inappropriate textbook-style calculations to evaluate statistics arising from repeated testing strategies during an epidemic.

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