scholarly journals Asymptotic frequency of shapes in supercritical branching trees

2016 ◽  
Vol 53 (4) ◽  
pp. 1143-1155 ◽  
Author(s):  
Giacomo Plazzotta ◽  
Caroline Colijn

Abstract The shapes of branching trees have been linked to disease transmission patterns. In this paper we use the general Crump‒Mode‒Jagers branching process to model an outbreak of an infectious disease under mild assumptions. Introducing a new class of characteristic functions, we are able to derive a formula for the limit of the frequency of the occurrences of a given shape in a general tree. The computational challenges concerning the evaluation of this formula are in part overcome using the jumping chronological contour process. We apply the formula to derive the limit of the frequency of cherries, pitchforks, and double cherries in the constant-rate birth‒death model, and the frequency of cherries under a nonconstant death rate.

2020 ◽  
Author(s):  
Angela Maria Cadavid Restrepo ◽  
Luis Furuya-Kanamori ◽  
Helen Mayfield ◽  
Eric J. Nilles ◽  
Colleen L. Lau

2021 ◽  
Vol 17 (1) ◽  
Author(s):  
Steve J. Bickley ◽  
Ho Fai Chan ◽  
Ahmed Skali ◽  
David Stadelmann ◽  
Benno Torgler

Abstract Background The ongoing COVID-19 pandemic has highlighted the vast differences in approaches to the control and containment of coronavirus across the world and has demonstrated the varied success of such approaches in minimizing the transmission of coronavirus. While previous studies have demonstrated high predictive power of incorporating air travel data and governmental policy responses in global disease transmission modelling, factors influencing the decision to implement travel and border restriction policies have attracted relatively less attention. This paper examines the role of globalization on the pace of adoption of international travel-related non-pharmaceutical interventions (NPIs) during the coronavirus pandemic. This study aims to offer advice on how to improve the global planning, preparation, and coordination of actions and policy responses during future infectious disease outbreaks with empirical evidence. Methods and data We analyzed data on international travel restrictions in response to COVID-19 of 185 countries from January to October 2020. We applied time-to-event analysis to examine the relationship between globalization and the timing of travel restrictions implementation. Results The results of our survival analysis suggest that, in general, more globalized countries, accounting for the country-specific timing of the virus outbreak and other factors, are more likely to adopt international travel restrictions policies. However, countries with high government effectiveness and globalization were more cautious in implementing travel restrictions, particularly if through formal political and trade policy integration. This finding is supported by a placebo analysis of domestic NPIs, where such a relationship is absent. Additionally, we find that globalized countries with high state capacity are more likely to have higher numbers of confirmed cases by the time a first restriction policy measure was taken. Conclusions The findings highlight the dynamic relationship between globalization and protectionism when governments respond to significant global events such as a public health crisis. We suggest that the observed caution of policy implementation by countries with high government efficiency and globalization is a by-product of commitment to existing trade agreements, a greater desire to ‘learn from others’ and also perhaps of ‘confidence’ in a government’s ability to deal with a pandemic through its health system and state capacity. Our results suggest further research is warranted to explore whether global infectious disease forecasting could be improved by including the globalization index and in particular, the de jure economic and political, and de facto social dimensions of globalization, while accounting for the mediating role of government effectiveness. By acting as proxies for a countries’ likelihood and speed of implementation for international travel restriction policies, such measures may predict the likely time delays in disease emergence and transmission across national borders.


Author(s):  
Gregory Gutin ◽  
Tomohiro Hirano ◽  
Sung-Ha Hwang ◽  
Philip R. Neary ◽  
Alexis Akira Toda

AbstractHow does social distancing affect the reach of an epidemic in social networks? We present Monte Carlo simulation results of a susceptible–infected–removed with social distancing model. The key feature of the model is that individuals are limited in the number of acquaintances that they can interact with, thereby constraining disease transmission to an infectious subnetwork of the original social network. While increased social distancing typically reduces the spread of an infectious disease, the magnitude varies greatly depending on the topology of the network, indicating the need for policies that are network dependent. Our results also reveal the importance of coordinating policies at the ‘global’ level. In particular, the public health benefits from social distancing to a group (e.g. a country) may be completely undone if that group maintains connections with outside groups that are not following suit.


2012 ◽  
Vol 54 (1-2) ◽  
pp. 23-36 ◽  
Author(s):  
E. K. WATERS ◽  
H. S. SIDHU ◽  
G. N. MERCER

AbstractPatchy or divided populations can be important to infectious disease transmission. We first show that Lloyd’s mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity.


2018 ◽  
Vol 38 (8) ◽  
pp. 930-941
Author(s):  
Peter J. Dodd ◽  
Jeff J. Pennington ◽  
Liza Bronner Murrison ◽  
David W. Dowdy

Introduction. Cost-effectiveness models for infectious disease interventions often require transmission models that capture the indirect benefits from averted subsequent infections. Compartmental models based on ordinary differential equations are commonly used in this context. Decision trees are frequently used in cost-effectiveness modeling and are well suited to describing diagnostic algorithms. However, complex decision trees are laborious to specify as compartmental models and cumbersome to adapt, limiting the detail of algorithms typically included in transmission models. Methods. We consider an approximation replacing a decision tree with a single holding state for systems where the time scale of the diagnostic algorithm is shorter than time scales associated with disease progression or transmission. We describe recursive algorithms for calculating the outcomes and mean costs and delays associated with decision trees, as well as design strategies for computational implementation. We assess the performance of the approximation in a simple model of transmission/diagnosis and its role in simplifying a model of tuberculosis diagnostics. Results. When diagnostic delays were short relative to recovery rates, our approximation provided a good account of infection dynamics and the cumulative costs of diagnosis and treatment. Proportional errors were below 5% so long as the longest delay in our 2-step algorithm was under 20% of the recovery time scale. Specifying new diagnostic algorithms in our tuberculosis model was reduced from several tens to just a few lines of code. Discussion. For conditions characterized by a diagnostic process that is neither instantaneous nor protracted (relative to transmission dynamics), this novel approach retains the advantages of decision trees while embedding them in more complex models of disease transmission. Concise specification and code reuse increase transparency and reduce potential for error.


2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Navavat Pipatsart ◽  
Wannapong Triampo ◽  
Charin Modchang

We presented adaptive random network models to describe human behavioral change during epidemics and performed stochastic simulations of SIR (susceptible-infectious-recovered) epidemic models on adaptive random networks. The interplay between infectious disease dynamics and network adaptation dynamics was investigated in regard to the disease transmission and the cumulative number of infection cases. We found that the cumulative case was reduced and associated with an increasing network adaptation probability but was increased with an increasing disease transmission probability. It was found that the topological changes of the adaptive random networks were able to reduce the cumulative number of infections and also to delay the epidemic peak. Our results also suggest the existence of a critical value for the ratio of disease transmission and adaptation probabilities below which the epidemic cannot occur.


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