scholarly journals Estimating the distribution of time to extinction of infectious diseases in mean-field approaches

2020 ◽  
Author(s):  
Maryam Aliee ◽  
Kat S. Rock ◽  
Matt J. Keeling
Keyword(s):  
Infectious Diseases ◽  
Stochastic Models ◽  
Mean Field ◽  
Practical Method ◽  
Deterministic Models ◽  
Recovery Processes ◽  
Time To Extinction ◽  
And Control ◽  
Field Approaches ◽  
Birth Death

AbstractA key challenge for many infectious diseases is to predict the time to extinction under specific interventions. In general this question requires the use of stochastic models which recognise the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when parameter uncertainty also needs to be incorporated. Deterministic models are often used for prediction as they are more tractable, however their inability to precisely reach zero infections makes forecasting extinction times problematic. Here, we study the extinction problem in deterministic models with the help of an effective “birth-death” description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth-death framework. We show these predictions agree very well with the results of stochastic models by analysing the simplified SIS dynamics as well as studying an example of more complex and realistic dynamics accounting for the infection and control of African sleeping sickness (Trypanosoma brucei gambiense).

scholarly journals Estimating the distribution of time to extinction of infectious diseases in mean-field approaches

2020 ◽  
Vol 17 (173) ◽  
pp. 20200540
Author(s):  
Maryam Aliee ◽  
Kat S. Rock ◽  
Matt J. Keeling
Keyword(s):  
Infectious Diseases ◽  
Stochastic Models ◽  
Mean Field ◽  
Practical Method ◽  
Deterministic Models ◽  
Recovery Processes ◽  
Time To Extinction ◽  
And Control ◽  
Field Approaches ◽  
Birth Death

A key challenge for many infectious diseases is to predict the time to extinction under specific interventions. In general, this question requires the use of stochastic models which recognize the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when parameter uncertainty also needs to be incorporated. Deterministic models are often used for prediction as they are more tractable; however, their inability to precisely reach zero infections makes forecasting extinction times problematic. Here, we study the extinction problem in deterministic models with the help of an effective ‘birth–death’ description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth–death framework. We show that these predictions agree very well with the results of stochastic models by analysing the simplified susceptible–infected–susceptible (SIS) dynamics as well as studying an example of more complex and realistic dynamics accounting for the infection and control of African sleeping sickness ( Trypanosoma brucei gambiense ).

scholarly journals A Stochastic Model for Malaria Transmission Dynamics

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Rachel Waema Mbogo ◽  
Livingstone S. Luboobi ◽  
John W. Odhiambo
Keyword(s):  
Infectious Diseases ◽  
Stochastic Model ◽  
Malaria Transmission ◽  
Stochastic Models ◽  
Continuous Time ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Infected Mosquito ◽  
Deterministic Models ◽  
Discrete State

Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis). In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp). The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.

Communicable and Other Infectious Diseases

2020 ◽  
Author(s):  
Markus Frischhut
Keyword(s):  
Public Health ◽  
European Union ◽  
Infectious Diseases ◽  
Disease Transmission ◽  
Eu Law ◽  
The European Union ◽  
Ethical Perspective ◽  
Health Measures ◽  
Environment Agency ◽  
And Control

This chapter discusses the most important features of EU law on infectious diseases. Communicable diseases not only cross borders, they also often require measures that cross different areas of policy because of different vectors for disease transmission. The relevant EU law cannot be attributed to one sectoral policy only, and thus various EU agencies participate in protecting public health. The key agency is the European Centre for Disease Prevention and Control. Other important agencies include the European Environment Agency; European Food Safety Authority; and the Consumers, Health, Agriculture and Food Executive Agency. However, while integration at the EU level has facilitated protection of the public's health, it also has created potential conflicts among the different objectives of the European Union. The internal market promotes the free movement of products, but public health measures can require restrictions of trade. Other conflicts can arise if protective public health measures conflict with individual human rights. The chapter then considers risk assessment and the different tools of risk management used in dealing with the challenges of infectious diseases. It also turns to the external and ethical perspective and the role the European Union takes in global health.

scholarly journals The impacts of COVID-19 preventive and control interventions on other infectious diseases in China

2021 ◽  
pp. 1-6
Author(s):  
Xiujuan Meng ◽  
Xun Huang ◽  
Feng Zhou ◽  
Yaowang Wang ◽  
Chunhui Li ◽  
...  
Keyword(s):  
Infectious Diseases ◽  
And Control

Potentiality of Mean-Field Approaches for Recrystallisation: Characterization of the Deformed State of Polycrystals

2004 ◽  
Vol 467-470 ◽  
pp. 33-38 ◽  
Author(s):  
Rénald Brenner ◽  
O. Castelnau ◽  
Brigitte Bacroix
Keyword(s):  
Mean Field ◽  
Mechanical State ◽  
Microstructural Parameters ◽  
Deformed State ◽  
The Mean ◽  
Field Approaches

The description of the mechanical state of a polycrystal is presented in the framework of the mean-field approaches and attention is paid to the fields heterogeneity. For nonlinear behaviours, the importance of the chosen model is emphasized with respect to relevant microstructural parameters for recrystallisation.

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