Bounds on the velocity of spread of infection for a spatially connected epidemic process

1980 ◽  
Vol 17 (03) ◽  
pp. 839-845 ◽  
Author(s):  
M. J. Faddy ◽  
I. H. Slorach
Keyword(s):  
Asymptotic Velocity ◽  
Epidemic Process ◽  
Lower Bounding ◽  
Stochastic Epidemic ◽  
Spread Of Infection

The simple (non-spatial) stochastic epidemic is generalised to allow infected individuals to move forward through a system of spatially connected colonies C 1, C 2, C 3, ·· ·each containing susceptible individuals. Upper and lower bounding processes are considered, to establish bounds on the asymptotic velocity of forward spread of the infection through these spatially connected colonies. These bounds are shown to be asymptotically equivalent under certain conditions, and some simulations reveal other features of the process.

Bounds on the velocity of spread of infection for a spatially connected epidemic process

1980 ◽  
Vol 17 (3) ◽  
pp. 839-845 ◽  
Author(s):  
M. J. Faddy ◽  
I. H. Slorach
Keyword(s):  
Asymptotic Velocity ◽  
Epidemic Process ◽  
Lower Bounding ◽  
Stochastic Epidemic ◽  
Spread Of Infection

The simple (non-spatial) stochastic epidemic is generalised to allow infected individuals to move forward through a system of spatially connected colonies C1, C2, C3, ·· ·each containing susceptible individuals. Upper and lower bounding processes are considered, to establish bounds on the asymptotic velocity of forward spread of the infection through these spatially connected colonies. These bounds are shown to be asymptotically equivalent under certain conditions, and some simulations reveal other features of the process.

On the asymptotic distribution of the size of a stochastic epidemic

1983 ◽  
Vol 20 (2) ◽  
pp. 390-394 ◽  
Author(s):  
Thomas Sellke
Keyword(s):  
Population Size ◽  
Asymptotic Distribution ◽  
Epidemic Process ◽  
Stochastic Epidemic ◽  
Original Number ◽  
Intuitive Proof

For a stochastic epidemic of the type considered by Bailey [1] and Kendall [3], Daniels [2] showed that ‘when the threshold is large but the population size is much larger, the distribution of the number remaining uninfected in a large epidemic has approximately the Poisson form.' A simple, intuitive proof is given for this result without use of Daniels's assumption that the original number of infectives is ‘small'. The proof is based on a construction of the epidemic process which is more explicit than the usual description.

scholarly journals To the question of the reasons for the activation of the epidemic process of Мeasles at the stage of elimination of infection and the forecast of the situation in the near and long term

2021 ◽  
Vol 20 (1) ◽  
pp. 50-55
Author(s):  
T. A. Platonova ◽  
A. A. Golubkova ◽  
S. S. Smirnova
Keyword(s):  
Mathematical Modeling ◽  
Vulnerable Groups ◽  
Medical Documentation ◽  
Epidemic Process ◽  
Population Immunity ◽  
Spread Of Infection ◽  
Measles Incidence ◽  
Observation Period

Introduction. Measles infection in recent years has become particularly relevant in connection with the registration of outbreaks of this disease in various territoriesof the Russian Federation and abroad.The aim of the study is to characterize the epidemic process of measles in a large industrial city in the near and long term with the use of modern mathematical modeling technologies for making new management decisions on infection control at the elimination stage.Materials and methods. The research materials were data from statistical reports of measles incidence in Yekaterinburg from 1950 to 2019 (70 years of follow-up), medical documentation of measles cases, population vaccination data (form No. 6 for 2000—2018 and outpatient maps of children under two years of age vaccinated against measles), results of screening for measles IgG ofmedical organizations, data of planned serological monitoringof population immunity to measles in «indicator» groups in the period from 2013 to 2017 and the results of mathematical modeling of measles incidence in different scenarios of its prevention.Results. Under the influence of vaccination, the epidemic process of measles in Yekaterinburg — a city with a population of 1.5million inhabitants-has undergone significant changes. During the observation period, the incidence decreased to sporadic levels, there was no indigenous measles, drifts from endemic areas had no consequences, the epidemic process was under control. However, outbreaks of 72 cases in 2016 and 90 cases in 2019 have changed our view of measles as a eradicated infection.Of the factors that led to the spread of infection in the foci, the most significant were the presence of measles-susceptible children and adults, including those previously vaccinated, mainly in the periods remote from vaccination and revaccination, defects in the clinical diagnosis of measlesin the first and subsequent cases, and violations in the organization and conduct of anti-epidemic measures. Conclusion. Based on the data of mathematical modeling of the epidemic process of measles with different combinations of its determinants, for the elimination of infection, it is necessary to ensure vaccination against measles at the age of 1 year and 6 years in 95—97.5%. In vulnerable groups for infection to discuss the introduction of routine revaccination among people up to 50 years of age with an interval of 10 years.

Some features of the epidemic spread of the new coronavirus infection (COVID-19) in the Rostov Region

2020 ◽  
Vol 11 (4) ◽  
pp. 99-106
Author(s):  
E. V. Kovalev ◽  
S. S. Slis ◽  
E. G. Yanovich ◽  
N. L. Pichurina ◽  
S. V. Volovikova ◽  
...  
Keyword(s):  
Process Intensification ◽  
Human Welfare ◽  
Epidemic Process ◽  
Regional Features ◽  
Rostov Region ◽  
Number Of Patients ◽  
Coronavirus Infection ◽  
Spread Of Infection ◽  
Very High ◽  
Epidemiological Situation

Purpose: to analyze the epidemiological situation for a new coronavirus infection (COVID-19), to identify some regional features of the Rostov region that contribute to spread of infection.Materials and methods: when assessing the epidemiological situation for a new coronavirus infection in the Rostov region, we used information provided by the Department of the Federal service for supervision of consumer protection and human welfare in the Rostov region. Processing of statistical data was performed by means of generally accepted method.Results: the spreading of a new coronavirus infection in the Rostov region is uneven in nature. When differentiating the territories of the region we identified groups of municipalities with a very high, medium and low number of patients. The administrative territories division of the Rostov region into the “Rostov urban agglomeration” and cluster of municipalities in which pronounced factors and conditions determining the “pendulum” migration of the population are absent, allow analyzing the specific features of the region and identification of territory with the highest risk of epidemic process intensification of a new coronavirus infection.Conclusions: the carried out differentiation of municipalities made it possible to identify and analyze some territorial features of the Rostov region, contributing to the spread of a new coronavirus infection. The obtained results could be used for development of measures aimed at reducing intensification of the epidemic process COVID-19 in condition infection. 

A note on perturbation techniques for epidemics

1971 ◽  
Vol 3 (2) ◽  
pp. 214-218
Author(s):  
H. E. Daniels
Keyword(s):  
Difference Equations ◽  
Zero Order ◽  
Similar Type ◽  
Perturbation Techniques ◽  
Epidemic Process ◽  
Stochastic Epidemic ◽  
Explicit Formulae

This note is prompted by the papers of Weiss (this Symposium) and Bailey (1968). Weiss develops a technique for approximation to the moments of an epidemic process by regarding them as expandable in powers of N-1 where N is the size of the population, assumed constant. He first considers the simple stochastic epidemic with no removals and obtains explicit formulae for the terms of order N-1, the zero order terms being the deterministic values. Bailey is concerned with a similar type of approximation and he derives explicit results to the same order. Bailey uses an eigenfunction approach whereas Weiss's method is more direct and perhaps easier to generalise. However, in attempting to extend the method to the case of a closed epidemic with removals Weiss is led to intractable difference equations.

A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models

1986 ◽  
Vol 18 (2) ◽  
pp. 289-310 ◽  
Author(s):  
Frank Ball
Keyword(s):  
Probabilistic Approach ◽  
Heterogeneous Population ◽  
Epidemic Models ◽  
Infectious Period ◽  
Unified Approach ◽  
Total Size ◽  
Epidemic Process ◽  
Stochastic Epidemic ◽  
General Stochastic

We provide a unified probabilistic approach to the distribution of total size and total area under the trajectory of infectives for a general stochastic epidemic with any specified distribution of the infectious period. The key tool is a Wald&s identity for the epidemic process. The generalisation of our results to epidemics spreading amongst a heterogeneous population is straightforward.

On the asymptotic distribution of the size of a stochastic epidemic

1983 ◽  
Vol 20 (02) ◽  
pp. 390-394 ◽  
Author(s):  
Thomas Sellke
Keyword(s):  
Population Size ◽  
Asymptotic Distribution ◽  
Epidemic Process ◽  
Stochastic Epidemic ◽  
Original Number ◽  
Intuitive Proof

For a stochastic epidemic of the type considered by Bailey [1] and Kendall [3], Daniels [2] showed that ‘when the threshold is large but the population size is much larger, the distribution of the number remaining uninfected in a large epidemic has approximately the Poisson form.' A simple, intuitive proof is given for this result without use of Daniels's assumption that the original number of infectives is ‘small'. The proof is based on a construction of the epidemic process which is more explicit than the usual description.

A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models

1986 ◽  
Vol 18 (02) ◽  
pp. 289-310 ◽  
Author(s):  
Frank Ball
Keyword(s):  
Probabilistic Approach ◽  
Heterogeneous Population ◽  
Epidemic Models ◽  
Infectious Period ◽  
Unified Approach ◽  
Total Size ◽  
Epidemic Process ◽  
Stochastic Epidemic ◽  
General Stochastic

We provide a unified probabilistic approach to the distribution of total size and total area under the trajectory of infectives for a general stochastic epidemic with any specified distribution of the infectious period. The key tool is a Wald&s identity for the epidemic process. The generalisation of our results to epidemics spreading amongst a heterogeneous population is straightforward.

A note on perturbation techniques for epidemics

1971 ◽  
Vol 3 (02) ◽  
pp. 214-218
Author(s):  
H. E. Daniels
Keyword(s):  
Difference Equations ◽  
Zero Order ◽  
Similar Type ◽  
Perturbation Techniques ◽  
Epidemic Process ◽  
Stochastic Epidemic ◽  
Explicit Formulae

This note is prompted by the papers of Weiss (this Symposium) and Bailey (1968). Weiss develops a technique for approximation to the moments of an epidemic process by regarding them as expandable in powers of N-1 where N is the size of the population, assumed constant. He first considers the simple stochastic epidemic with no removals and obtains explicit formulae for the terms of order N -1, the zero order terms being the deterministic values. Bailey is concerned with a similar type of approximation and he derives explicit results to the same order. Bailey uses an eigenfunction approach whereas Weiss's method is more direct and perhaps easier to generalise. However, in attempting to extend the method to the case of a closed epidemic with removals Weiss is led to intractable difference equations.

Registration of animal rabies in Krasnodar region

2020 ◽  
pp. 3-4
Author(s):  
Oleg Yu. Chernykh ◽  
◽  
Vadim A. Bobrov ◽  
Sergey N. Zabashta ◽  
Roman A. Krivonos ◽  
...  
Keyword(s):  
Urban Form ◽  
Animal Species ◽  
Farm Animals ◽  
Natural Focus ◽  
Dead End ◽  
Wide Range ◽  
Epizootic Process ◽  
Krasnodar Region ◽  
Spread Of Infection ◽  
Reporting Data

Rabies remains a constant threat to humanity in many parts of the world. At the same time, scientifically grounded antiepizootic measures should be based on the peculiarities of the regional epizootology of this zooanthroponosis. The authors studied the epizootological and statistical reporting data of the Kropotkin Regional Veterinary Laboratory, presented an analysis of the registration of rabies in animals in Krasnodar region. From the obtained data, it should be noted that despite the wide range of animals involved in the epizootic process of rabies infection in Krasnodar region, dogs, cats and foxes play a major role in the reservation and spread of infection, which account for 78.6. Of the total number of registered cases, 15.5% falls on foxes, that indicates the natural focus of the disease, along with the manifestation of the disease in an urban form. At the same time, stray and neglected dogs and cats, which occupy a significant place among the total number of sick animals, are also sources and spread of the infection. Thus farm animals (8.3% of the total number of infected animals) are a biological dead end for the infection. Isolated cases of the disease were noted in muskrat, donkey, raccoon, raccoon dog, marten, ferret and jackal. The authors also established the specific morbidity of various animal species with rabies infection, that is an important aspect in the development and implementation of antiepizootic measures complex

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