scholarly journals Health safety nets can break cycles of poverty and disease: a stochastic ecological model

2011 ◽  
Vol 8 (65) ◽  
pp. 1796-1803 ◽  
Author(s):  
Mateusz M. Pluciński ◽  
Calistus N. Ngonghala ◽  
Matthew H. Bonds
Keyword(s):  
Stochastic Model ◽  
Deterministic Model ◽  
Initial Conditions ◽  
Basin Of Attraction ◽  
Safety Net ◽  
Poverty Traps ◽  
Poverty Trap ◽  
Theoretical Frameworks ◽  
Deterministic Models ◽  
The Impact

The persistence of extreme poverty is increasingly attributed to dynamic interactions between biophysical processes and economics, though there remains a dearth of integrated theoretical frameworks that can inform policy. Here, we present a stochastic model of disease-driven poverty traps. Whereas deterministic models can result in poverty traps that can only be broken by substantial external changes to the initial conditions, in the stochastic model there is always some probability that a population will leave or enter a poverty trap. We show that a ‘safety net’, defined as an externally enforced minimum level of health or economic conditions, can guarantee ultimate escape from a poverty trap, even if the safety net is set within the basin of attraction of the poverty trap, and even if the safety net is only in the form of a public health measure. Whereas the deterministic model implies that small improvements in initial conditions near the poverty-trap equilibrium are futile, the stochastic model suggests that the impact of changes in the location of the safety net on the rate of development may be strongest near the poverty-trap equilibrium.

scholarly journals Noise-induced bistability in the quasineutral coexistence of viral RNA under different replication modes

2018 ◽  
Author(s):  
Josep Sardanyés ◽  
Andreu Arderiu ◽  
Santiago F. Elena ◽  
Tomás Alarcón
Keyword(s):  
Viral Replication ◽  
Evolutionary Dynamics ◽  
Rna Viruses ◽  
Initial Conditions ◽  
Rna Replication ◽  
Viral Rna ◽  
Stochastic Simulations ◽  
Strong Impact ◽  
Deterministic Models ◽  
The Impact

Evolutionary and dynamical investigations on real viral populations indicate that RNA replication can range between two extremes given by so-called stamping machine replication (SMR) and geometric replication (GR). The impact of asymmetries in replication for single-stranded, (+) sense RNA viruses has been up to now studied with deterministic models. However, viral replication should be better described by including stochasticity, since the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasineutral coexistence scenario, with a line of fixed points involving different strands’ equilibrium ratios depending on the initial conditions. Recent research on the quasineutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alters the mean-field scenario, and one of the two species outcompetes the other one. In this manuscript we study this phenomenon for RNA viral replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNA, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication.

scholarly journals Noise-induced bistability in the quasi-neutral coexistence of viral RNAs under different replication modes

2018 ◽  
Vol 15 (142) ◽  
pp. 20180129 ◽  
Author(s):  
Josep Sardanyés ◽  
Andreu Arderiu ◽  
Santiago F. Elena ◽  
Tomás Alarcón
Keyword(s):  
Evolutionary Dynamics ◽  
Rna Viruses ◽  
Initial Conditions ◽  
Rna Replication ◽  
Viral Rna ◽  
Stochastic Simulations ◽  
Strong Impact ◽  
Deterministic Models ◽  
Viral Rnas ◽  
The Impact

Evolutionary and dynamical investigations into real viral populations indicate that RNA replication can range between the two extremes represented by so-called ‘stamping machine replication’ (SMR) and ‘geometric replication’ (GR). The impact of asymmetries in replication for single-stranded (+) sense RNA viruses has been mainly studied with deterministic models. However, viral replication should be better described by including stochasticity, as the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasi-neutral coexistence scenario, with a line of fixed points involving different strands' equilibrium ratios depending on the initial conditions. Recent research into the quasi-neutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alter the mean-field scenario, and one of the two species outcompetes the other. In this article, we study this phenomenon for viral RNA replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNAs, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication.

CONFLICTS, CALAMITIES AND NUTRITIONAL POVERTY TRAPS IN A PEASANT ECONOMY: EVIDENCE FROM RURAL CHINA 1929–1933

2019 ◽  
pp. 1-31 ◽  
Author(s):  
LI ZHOU ◽  
JIE SUN ◽  
CALUM GREIG TURVEY
Keyword(s):  
Rural China ◽  
Agricultural Productivity ◽  
Poverty Traps ◽  
Poverty Trap ◽  
Anecdotal Evidence ◽  
Agricultural Economy ◽  
Conflict Zones ◽  
Nutrition Intake ◽  
The Many ◽  
The Impact

This paper uses data compiled by John Lossing Buck from his rural China survey conducted between 1929 and 1933 to analyze the impact of weather calamities and conflict on agricultural productivity, farm wages and nutrition intake. Our results support the conditions required for a Nutritional Poverty Trap (NPT) to be present, while anecdotal evidence points to the potential presence of a nutritional poverty trap for large segments of China’s agricultural economy. We find a lagged effect of climate shock on nutrition, but find no evidence that the many conflicts of the day affected nutrition. This is more likely due to the avoidance of conflict zones by surveyors, but may also support the notion that the effects from conflicts were local and short-lived due to the resilience of farmers.

Whole Cell Stochastic Model Reproduces the Irregularities Found in the Membrane Potential of Bursting Neurons

2005 ◽  
Vol 94 (2) ◽  
pp. 1169-1179 ◽  
Author(s):  
Pedro V. Carelli ◽  
Marcelo B. Reyes ◽  
José C. Sartorelli ◽  
Reynaldo D. Pinto
Keyword(s):  
Membrane Potential ◽  
Stochastic Model ◽  
Motor Neurons ◽  
Deterministic Model ◽  
Initial Conditions ◽  
Cytosolic Calcium ◽  
Type Model ◽  
Whole Cell ◽  
Nonlinear Properties ◽  
Oscillatory Dynamics

Irregular intrinsic behavior of neurons seems ubiquitous in the nervous system. Even in circuits specialized to provide periodic and reliable patterns to control the repetitive activity of muscles, such as the pyloric central pattern generator (CPG) of the crustacean stomatogastric ganglion (STG), many bursting motor neurons present irregular activity when deprived from synaptic inputs. Moreover, many authors attribute to these irregularities the role of providing flexibility and adaptation capabilities to oscillatory neural networks such as CPGs. These irregular behaviors, related to nonlinear and chaotic properties of the cells, pose serious challenges to developing deterministic Hodgkin-Huxley-type (HH-type) conductance models. Only a few deterministic HH-type models based on experimental conductance values were able to show such nonlinear properties, but most of these models are based on slow oscillatory dynamics of the cytosolic calcium concentration that were never found experimentally in STG neurons. Based on an up-to-date single-compartment deterministic HH-type model of a STG neuron, we developed a stochastic HH-type model based on the microscopic Markovian states that an ion channel can achieve. We used tools from nonlinear analysis to show that the stochastic model is able to express the same kind of irregularities, sensitivity to initial conditions, and low dimensional dynamics found in the neurons isolated from the STG. Without including any nonrealistic dynamics in our whole cell stochastic model, we show that the nontrivial dynamics of the membrane potential naturally emerge from the interplay between the microscopic probabilistic character of the ion channels and the nonlinear interactions among these elements. Moreover, the experimental irregular behavior is reproduced by the stochastic model for the same parameters for which the membrane potential of the original deterministic model exhibits periodic oscillations.

scholarly journals The effect of population structure on the emergence of drug resistance during influenza pandemics

2007 ◽  
Vol 4 (16) ◽  
pp. 893-906 ◽  
Author(s):  
Florence Débarre ◽  
Sebastian Bonhoeffer ◽  
Roland R Regoes
Keyword(s):  
Drug Resistance ◽  
Population Structure ◽  
Stochastic Model ◽  
Large Scale ◽  
Deterministic Model ◽  
Influenza Pandemics ◽  
Large Populations ◽  
Demographic Processes ◽  
Fragmented Population ◽  
The Impact

The spread of H5N1 avian influenza and the recent high numbers of confirmed human cases have raised international concern about the possibility of a new pandemic. Therefore, antiviral drugs are now being stockpiled to be used as a first line of defence. The large-scale use of antivirals will however exert a strong selection pressure on the virus, and may lead to the emergence of drug-resistant strains. A few mathematical models have been developed to assess the emergence of drug resistance during influenza pandemics. These models, however, neglected the spatial structure of large populations and the stochasticity of epidemic and demographic processes. To assess the impact of population structure and stochasticity, we modify and extend a previous model of influenza epidemics into a metapopulation model which takes into account the division of large populations into smaller units, and develop deterministic and stochastic versions of the model. We find that the dynamics in a fragmented population is less explosive, and, as a result, prophylaxis will prevent more infections and lead to fewer resistant cases in both the deterministic and stochastic model. While in the deterministic model the final level of resistance during treatment is not affected by fragmentation, in the stochastic model it is. Our results enable us to qualitatively extrapolate the prediction of deterministic, homogeneous-mixing models to more realistic scenarios.

scholarly journals Engineering a seven enzyme biotransformation using mathematical modelling and characterized enzyme parts

2019 ◽  
Author(s):  
William Finnigan ◽  
Rhys Cutlan ◽  
Radka Snajdrova ◽  
Joseph P. Adams ◽  
Jennifer A. Littlechild ◽  
...  
Keyword(s):  
Process Model ◽  
Deterministic Model ◽  
Cofactor Regeneration ◽  
Process Models ◽  
Model Quality ◽  
Deterministic Models ◽  
Enzyme Reactions ◽  
Enzyme Cascades ◽  
The Impact

AbstractMulti-step enzyme reactions offer considerable cost and productivity benefits. Process models offer a route to understanding the complexity of these reactions, and allow for their optimization. Despite the increasing prevalence of multi-step biotransformations, there are few examples of process models for enzyme reactions. From a toolbox of characterized enzyme parts, we demonstrate the construction of a process model for a seven enzyme, three step biotransformation using isolated enzymes. Enzymes for cofactor regeneration were employed to make thisin vitroreaction economical. Good modelling practice was critical in evaluating the impact of approximations and experimental error. We show that the use and validation of process models was instrumental in realizing and removing process bottlenecks, identifying divergent behavior, and for the optimization of the entire reaction using a genetic algorithm. We validated the optimized reaction to demonstrate that complex multi-step reactions with cofactor recycling involving at least seven enzymes can be reliably modelled and optimized.Significance statementThis study examines the challenge of modeling and optimizing multi-enzyme cascades. We detail the development, testing and optimization of a deterministic model of a three enzyme cascade with four cofactor regeneration enzymes. Significantly, the model could be easily used to predict the optimal concentrations of each enzyme in order to get maximum flux through the cascade. This prediction was strongly validated experimentally. The success of our model demonstrates that robust models of systems of at least seven enzymes are readily achievable. We highlight the importance of following good modeling practice to evaluate model quality and limitations. Examining deviations from expected behavior provided additional insight into the model and enzymes. This work provides a template for developing larger deterministic models of enzyme cascades.

scholarly journals Stochastic and deterministic analysis of SIS household epidemics

2006 ◽  
Vol 38 (4) ◽  
pp. 943-968 ◽  
Author(s):  
Peter Neal
Keyword(s):  
Stochastic Model ◽  
Law Of Large Numbers ◽  
Deterministic Model ◽  
Endemic Equilibrium ◽  
Infectious Period ◽  
Deterministic Models ◽  
Deterministic Analysis ◽  
Large Numbers ◽  
The Mean ◽  
Deterministic Limit

We analyse SIS epidemics among populations partitioned into households. The analysis considers both the stochastic and deterministic models and, unlike in previous analyses, we consider general infectious period distributions. For the deterministic model, we prove the existence of an endemic equilibrium for the epidemic if and only if the threshold parameter, R*, is greater than 1. Furthermore, by utilising Markov chains we show that the total number of infectives converges to the endemic equilibrium as t → ∞. For the stochastic model, we prove a law of large numbers result for the convergence, to the deterministic limit, of the mean number of infectives per household. This is followed by the derivation of a Gaussian limit process for the fluctuations of the stochastic model.

scholarly journals Dynamics of cholera epidemic models in fluctuating environments

2020 ◽  
Vol 21 (02) ◽  
pp. 2150011
Author(s):  
Tuan Anh Phan ◽  
Jianjun Paul Tian ◽  
Bixiang Wang
Keyword(s):  
Stochastic Model ◽  
Basic Reproduction Number ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Deterministic Models ◽  
Dynamical Behaviors ◽  
All Solutions ◽  
Number Formula ◽  
Asymptotical Analysis ◽  
The Basic Reproduction Number

Based on our deterministic models for cholera epidemics, we propose a stochastic model for cholera epidemics to incorporate environmental fluctuations which is a nonlinear system of Itô stochastic differential equations. We conduct an asymptotical analysis of dynamical behaviors for the model. The basic stochastic reproduction value [Formula: see text] is defined in terms of the basic reproduction number [Formula: see text] for the corresponding deterministic model and noise intensities. The basic stochastic reproduction value determines the dynamical patterns of the stochastic model. When [Formula: see text], the cholera infection will extinct within finite periods of time almost surely. When [Formula: see text], the cholera infection will persist most of time, and there exists a unique stationary ergodic distribution to which all solutions of the stochastic model will approach almost surely as noise intensities are bounded. When the basic reproduction number [Formula: see text] for the corresponding deterministic model is greater than 1, and the noise intensities are large enough such that [Formula: see text], the cholera infection is suppressed by environmental noises. We carry out numerical simulations to illustrate our analysis, and to compare with the corresponding deterministic model. Biological implications are pointed out.

Burden of Congenital Rubella Syndrome (CRS) in Bangladesh: Systematic Review of Existing Literature and Transmission Modelling of Seroprevalence Studies

2020 ◽  
Vol 20 (3) ◽  
pp. 284-290
Author(s):  
Jocelyn Chan ◽  
Yue Wu ◽  
James Wood ◽  
Mohammad Muhit ◽  
Mohammed K. Mahmood ◽  
...  
Keyword(s):  
Systematic Review ◽  
Deterministic Model ◽  
Case Series ◽  
Controlled Vocabulary ◽  
Congenital Rubella Syndrome ◽  
Free Text ◽  
Childbearing Age ◽  
Vaccination Programs ◽  
Congenital Rubella ◽  
The Impact

Background and Objectives: Congenital Rubella Syndrome (CRS) is the leading cause of vaccine-preventable congenital anomalies. Comprehensive country-level data on the burden of CRS in low and middle-income countries, such as Bangladesh, are scarce. This information is essential for assessing the impact of rubella vaccination programs. We aim to systematically review the literature on the epidemiology of CRS and estimate the burden of CRS in Bangladesh. Methods: We conducted a systematic review of existing literature and transmission modelling of seroprevalence studies to estimate the pre-vaccine period burden of CRS in Bangladesh. OVID Medline (1948 – 23 November 2016) and OVID EMBASE (1974 – 23 November 2016) were searched using a combination of the database-specific controlled vocabulary and free text terms. We used an age-stratified deterministic model to estimate the pre-vaccination burden of CRS in Bangladesh. Findings: Ten articles were identified, published between 2000 and 2014, including seven crosssectional studies, two case series and one analytical case-control study. Rubella seropositivity ranged from 47.0% to 86.0% among all age population. Rubella sero–positivity increased with age. Rubella seropositivity among women of childbearing age was 81.0% overall. The estimated incidence of CRS was 0·99 per 1,000 live births, which corresponds to approximately 3,292 CRS cases annually in Bangladesh. Conclusion: The estimated burden of CRS in Bangladesh during the pre-vaccination period was high. This will provide important baseline information to assess the impact and cost-effectiveness of routine rubella immunisation, introduced in 2012 in Bangladesh.

scholarly journals On Kaufmann's theory of the impact of the pianoforte hammer

1920 ◽  
Vol 97 (682) ◽  
pp. 99-110 ◽  
Keyword(s):  
Initial Conditions ◽  
Practical Importance ◽  
Prima Facie ◽  
Point Of View ◽  
Infinite Length ◽  
Modes Of Vibration ◽  
Rigorous Treatment ◽  
The Subject ◽  
Set Up ◽  
The Impact

The theory of the vibrations of the pianoforte string put forward by Kaufmann in a well-known paper has figured prominently in recent discussions on the acoustics of this instrument. It proceeds on lines radically different from those adopted by Helmholtz in his classical treatment of the subject. While recognising that the elasticity of the pianoforte hammer is not a negligible factor, Kaufmann set out to simplify the mathematical analysis by ignoring its effect altogether, and treating the hammer as a particle possessing only inertia without spring. The motion of the string following the impact of the hammer is found from the initial conditions and from the functional solutions of the equation of wave-propagation on the string. On this basis he gave a rigorous treatment of two cases: (1) a particle impinging on a stretched string of infinite length, and (2) a particle impinging on the centre of a finite string, neither of which cases is of much interest from an acoustical point of view. The case of practical importance treated by him is that in which a particle impinges on the string near one end. For this case, he gave only an approximate theory from which the duration of contact, the motion of the point struck, and the form of the vibration-curves for various points of the string could be found. There can be no doubt of the importance of Kaufmann’s work, and it naturally becomes necessary to extend and revise his theory in various directions. In several respects, the theory awaits fuller development, especially as regards the harmonic analysis of the modes of vibration set up by impact, and the detailed discussion of the influence of the elasticity of the hammer and of varying velocities of impact. Apart from these points, the question arises whether the approximate method used by Kaufmann is sufficiently accurate for practical purposes, and whether it may be regarded as applicable when, as in the pianoforte, the point struck is distant one-eighth or one-ninth of the length of the string from one end. Kaufmann’s treatment is practically based on the assumption that the part of the string between the end and the point struck remains straight as long as the hammer and string remain in contact. Primâ facie , it is clear that this assumption would introduce error when the part of the string under reference is an appreciable fraction of the whole. For the effect of the impact would obviously be to excite the vibrations of this portion of the string, which continue so long as the hammer is in contact, and would also influence the mode of vibration of the string as a whole when the hammer loses contact. A mathematical theory which is not subject to this error, and which is applicable for any position of the striking point, thus seems called for.

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