scholarly journals On Deterministic and Stochastic Multiple Pathogen Epidemic Models

Epidemiologia ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 325-337
Author(s):  
Fernando Vadillo
Keyword(s):  
Variable Coefficients ◽  
Epidemic Models ◽  
Kolmogorov Equation ◽  
The Finite Element Method ◽  
Persistence Time ◽  
Main Challenge ◽  
Stochastic Epidemic ◽  
The Mean ◽  
Backward Kolmogorov Equation ◽  
Multiple Pathogen

In this paper, we consider a stochastic epidemic model with two pathogens. In order to analyze the coexistence of two pathogens, we compute numerically the expectation time until extinction (the mean persistence time), which satisfies a stationary partial differential equation with degenerate variable coefficients, related to backward Kolmogorov equation. I use the finite element method in order to solve this equation, and we implement it in FreeFem++. The main conclusion of this paper is that the deterministic and stochastic epidemic models differ considerably in predicting coexistence of the two diseases and in the extinction outcome of one of them. Now, the main challenge would be to find an explanation for this result.

The cost of a general stochastic epidemic

1972 ◽  
Vol 9 (02) ◽  
pp. 257-269 ◽  
Author(s):  
J. Gani ◽  
D. Jerwood
Keyword(s):  
Recursive Equation ◽  
Stieltjes Transform ◽  
Stochastic Epidemic ◽  
The Mean ◽  
The Cost ◽  
Mean Cost ◽  
General Stochastic

This paper is concerned with the cost Cis = aWis + bTis (a, b > 0) of a general stochastic epidemic starting with i infectives and s susceptibles; Tis denotes the duration of the epidemic, and Wis the area under the infective curve. The joint Laplace-Stieltjes transform of (Wis, Tis ) is studied, and a recursive equation derived for it. The duration Tis and its mean Nis are considered in some detail, as are also Wis and its mean Mis . Using the results obtained, bounds are found for the mean cost of the epidemic.

Stationary and Transient Response of Cylindrical Shells Under Random Excitation

1988 ◽  
Vol 110 (2) ◽  
pp. 205-209
Author(s):  
A. V. Singh
Keyword(s):  
Transient Response ◽  
Random Vibration ◽  
Time History ◽  
Wide Band ◽  
Random Excitation ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
History Of ◽  
The Mean ◽  
Random Vibration Analysis

This paper presents the random vibration analysis of a simply supported cylindrical shell under a ring load which is uniform around the circumference. The time history of the excitation is assumed to be a stationary wide-band random process. The finite element method and the condition of symmetry along the length of the cylinder are used to calculate the natural frequencies and associated mode shapes. Maximum values of the mean square displacements and velocities occur at the point of application of the load. It is seen that the transient response of the shell under wide band stationary excitation is nonstationary in the initial stages and approaches the stationary solution for large value of time.

On interarrival times in simple stochastic epidemic models

1982 ◽  
Vol 19 (4) ◽  
pp. 835-841
Author(s):  
Grace Yang ◽  
C. L. Chiang
Keyword(s):  
Probability Distributions ◽  
Asymptotic Distributions ◽  
Epidemic Models ◽  
Stochastic Epidemic Models ◽  
Stochastic Epidemic ◽  
Interarrival Times

The probability distributions of the size and the duration of simple stochastic epidemic models are well known. However, in most instances, the solutions are too complicated to be of practical use. In this note, interarrival times of the infectives are utilized to study asymptotic distributions of the duration of the epidemic for a class of simple epidemic models. A brief summary of the results on simple epidemic models in terms of interarrival times is included.

scholarly journals Persistence-time estimation for some stochastic SIS epidemic models

2015 ◽  
Vol 20 (9) ◽  
pp. 2933-2947 ◽  
Author(s):  
Francisco de la Hoz ◽  
Anna Doubova ◽  
Fernando Vadillo
Keyword(s):  
Time Estimation ◽  
Epidemic Models ◽  
Persistence Time ◽  
Sis Epidemic

scholarly journals Multiple shooting method in stability analysis of non-prismatic multi-segment columns

2013 ◽  
Vol 12 (4) ◽  
pp. 225-232
Author(s):  
Ryszard Hołubowski ◽  
Andrzej Merena
Keyword(s):  
Finite Element Method ◽  
Stability Analysis ◽  
Shooting Method ◽  
High Efficiency ◽  
Variable Coefficients ◽  
Multiple Shooting ◽  
System Of Differential Equations ◽  
The Finite Element Method ◽  
Concentrated Force ◽  
Multiple Shooting Method

The application of multiple shooting method in stability analysis of non-prismatic multi-segment columns with pinned ends loaded with a concentrated force applied to the upper node has been presented. Numerical analyses were carried out for an exemplary three-segment column by solving the system of differential equations with variable coefficients and parameter. The results were compared with the solution obtained by using SOFiSTiK software based on the finite element method. The analyses show that considering the stiffness changes along the length can have a significant influence on the values of critical loads and thus change the resistance of the column. The advantage of the proposed method is its high efficiency and easy description of stiffness changes.

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