Epidemics with carriers: The large population approximation

1967 ◽  
Vol 4 (02) ◽  
pp. 257-263 ◽  
Author(s):  
Hugh M. Pettigrew ◽  
George H. Weiss
Keyword(s):  
Latent Period ◽  
Large Population ◽  
Single Type ◽  
Exponential Distributions ◽  
Epidemic Size ◽  
Negative Exponential

This paper applies the constant population approximation to the study of epidemics which involve more than a single type of infective. An example of this would be a situation in which both clinically infected individuals and subclinically infected individuals or carriers are present. We derive equations for the expected numbers of clinically infected individuals and carriers at any time t for the model with zero latent period and infectious periods having negative exponential distributions. From these equations we derive conditions under which a unimodal incidence curve can result, and expressions for the expected total epidemic size.

Epidemics with carriers: The large population approximation

1967 ◽  
Vol 4 (2) ◽  
pp. 257-263 ◽  
Author(s):  
Hugh M. Pettigrew ◽  
George H. Weiss
Keyword(s):  
Latent Period ◽  
Large Population ◽  
Single Type ◽  
Exponential Distributions ◽  
Epidemic Size ◽  
Negative Exponential

This paper applies the constant population approximation to the study of epidemics which involve more than a single type of infective. An example of this would be a situation in which both clinically infected individuals and subclinically infected individuals or carriers are present.We derive equations for the expected numbers of clinically infected individuals and carriers at any time t for the model with zero latent period and infectious periods having negative exponential distributions. From these equations we derive conditions under which a unimodal incidence curve can result, and expressions for the expected total epidemic size.

A semi-Markov storage model

1973 ◽  
Vol 5 (02) ◽  
pp. 362-378 ◽  
Author(s):  
Jerome Senturia ◽  
Prem S. Puri
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
Laplace Transforms ◽  
Exact Distribution ◽  
Exponential Distributions ◽  
Random Inputs ◽  
Storage Model ◽  
Semi Markov Process ◽  
Negative Exponential ◽  
Independent Identically Distributed

In this paper a storage model is described in which fluctuations in the content are governed by a sequence of independent identically distributed (i.i.d.) random inputs and i.i.d. random releases. This sequence proceeds according to an underlying semi-Markov process. Laplace transforms of the exact distribution of the content are given for the case of negative exponential distributions for both inputs and releases. Exact expressions for limiting (in time) content distributions are found. In the general case, the asymptotic behavior of the content is described for critical and supercritical limiting conditions.

Multivariate birth-and-death processes as approximations to epidemic processes

1973 ◽  
Vol 10 (1) ◽  
pp. 15-26 ◽  
Author(s):  
D. A. Griffiths
Keyword(s):  
Transient Process ◽  
Branching Process ◽  
Large Population ◽  
Disease Spread ◽  
Death Process ◽  
Birth And Death Process ◽  
Birth And Death Processes ◽  
Epidemic Size

This paper presents the theory of a multivariate birth-and-death process and its representation as a branching process. The bivariate linear birth-and-death process may be used as a model for various epidemic situations involving two types of infective. Various properties of the transient process are discussed and the distribution of epidemic size is investigated. For the case of a disease spread solely by carriers when the two types of infective are carriers and clinical infectives the large population version of a model proposed by Downton (1968) is further developed and shown under appropriate circumstances to closely approximate Downton's model.

Perspectives on the age and distribution of large wood in riparian carbon pools

2002 ◽  
Vol 59 (3) ◽  
pp. 578-585 ◽  
Author(s):  
Richard P Guyette ◽  
William G Cole ◽  
Daniel C Dey ◽  
Rose-Marie Muzika
Keyword(s):  
Woody Debris ◽  
Age Distribution ◽  
Terrestrial Ecosystems ◽  
Large Wood ◽  
Riparian Ecosystems ◽  
Riparian Areas ◽  
Exponential Distributions ◽  
Drainage Patterns ◽  
Order Of Magnitude ◽  
Negative Exponential

Most knowledge of carbon budgets is derived from the productivity and sequestration of carbon in terrestrial and marine ecosystems. Less is known of carbon stored in riparian areas associated with lakes and rivers. Case studies of the age distribution of carbon in aquatic large wood (Clw) from two different landscapes with different drainage patterns were established using tree-ring and 14C dating. Cumulative negative exponential distributions of the age of Clw ranged over periods from 1000 to 9485 years. Large woody debris had mean residence times of 261 years in small oligotrophic lakes and 350–800 years in a stream reach. Large wood can reside for an order of magnitude longer in freshwater–riparian ecosystems than in comparable above-ground terrestrial ecosystems. Although riparian areas make up only a small fraction of most landscapes, they may account for a relatively larger proportion of aged Clw than is stored above ground in terrestrial ecosystems.

Regenerative stochastic processes

1955 ◽  
Vol 232 (1188) ◽  
pp. 6-31 ◽  
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Probability Distribution ◽  
Stochastic Processes ◽  
Wide Class ◽  
Initial Conditions ◽  
Limiting Distribution ◽  
Regenerative Processes ◽  
Exponential Distributions ◽  
Negative Exponential

A wide class of stochastic processes, called regenerative, is defined, and it is shown that under general conditions the instantaneous probability distribution of such a process tends with time to a unique limiting distribution, whatever the initial conditions. The general results are then applied to 'S.M.-processes’, a generalization of Markov chains, and it is shown that the limiting distribution of the process may always be obtained by assuming negative exponential distributions for the ‘waits’ in the different ‘states’. Lastly, the behaviour of integrals of regenerative processes is considered and, amongst other results, an ergodic and a multi-dimensional central limit theorem are proved.

scholarly journals A New Mathematical Approach for the Estimation of epidemic Model Parameters with Demonstration on COVID-19 Pandemic in Libya

2020 ◽  
Author(s):  
Mohamed E Saleh ◽  
Zeinab Elmehdi Saleh
Keyword(s):  
Exponential Function ◽  
Epidemic Model ◽  
Model Parameters ◽  
Cumulative Number ◽  
Epidemic Spread ◽  
Exponential Distributions ◽  
Negative Exponential Function ◽  
Seir Model ◽  
Start Date ◽  
Negative Exponential

Background: The SEIR model or a variation of it is commonly used to study epidemic spread and make predictions on how it evolves. It is used to guide officials in their response to an epidemic. This research demonstrates an effective and simple approach that estimates the parameters of any variations of the SEIR model. This new technique will be demonstrated on the spread of COVID-19 in Libya. Methods: A five compartmental epidemic model is used to model the COVID-19 pandemic in Libya. Two sets of data are needed to evaluate the model parameters, the cumulative number of symptomatic cases and the total number of active cases. This data along with the assumption that the cumulative number of symptomatic cases grows exponentially, to determine most of the model parameters. Results: Libya epidemic start-date was estimated as t_o=-18.5 days, corresponding to May 5th. We mathematically demonstrated that the number of active cases follows two competing exponential distributions: a positive exponential function, measuring how many new cases are added, and a negative exponential function, measuring how many cases recovered. From this distribution we showed that the average recovery time is 48 days, and the incubation period is 15.2 days. Finally, the productive number was estimated as R0 = 7.6. Conclusions: With only the cumulative number of cases and the total number of active cases of COVID19, several important SEIR model parameters can be measured effectively. This approach can be applied for any infectious disease epidemic anywhere in the world.

Edge-based SEIR dynamics with recovery rate in latent period on complex networks

2020 ◽  
Vol 31 (04) ◽  
pp. 2050057
Author(s):  
Rong Zhou ◽  
Qingchu Wu
Keyword(s):  
Latent Period ◽  
Recovery Rate ◽  
Stochastic Simulations ◽  
Epidemic Threshold ◽  
Seir Model ◽  
Scale Free ◽  
Epidemic Size ◽  
Final Epidemic Size ◽  
Full Analysis ◽  
Edge Based

Disease and information spreading on social and information networks have often been described by ordinary differential equations. A recent research by the authors [Y. Wang et al., Commun. Nonlinear Sci. Numer. Simulat. 45, 35 (2017).] presented an analysis of susceptible-exposed-infected-recovered (SEIR) model with and without infectious force in latent period. We present a full analysis in the more general scenario where the exposed nodes can get vaccinated or recovered. The basic reproduction number and the final epidemic size are theoretically derived. Compared to the standard SEIR model without recovery rate in latent period, our results reveal that both the recovery rate in latent period and the length of latent period can increase the epidemic threshold and inhibit the epidemic outbreak. In addition, the model predictions agree well with the continuous-time stochastic simulations in Erdős–Rényi random graphs and scale-free configuration networks.

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