scholarly journals The Milwaukee Cryptosporidium outbreak: assessment of incubation time and daily attack rate

2004 ◽  
Vol 2 (2) ◽  
pp. 59-69 ◽  
Author(s):  
Mukul Gupta ◽  
Charles N. Haas
Keyword(s):  
Incubation Time ◽  
Time Distribution ◽  
Time Course ◽  
Equation System ◽  
Differential Equation System ◽  
Epidemic Curve ◽  
Force Of Infection ◽  
Disease Occurrence ◽  
Functional Forms ◽  
Precise Assessment

The time course of reported illnesses (epidemic curve) in the 1993 Milwaukee outbreak of cryptosporidiosis was analysed using a dynamic model considering time variant force of infection and incubation time distributions. Different functional forms for the force of infection and incubation time distribution were tested. The resulting model is a coupled integro-differential equation system. These models gave a good fit to the data, although depending upon the functional forms of the underlying distributions, different incubation time and force of infection curves were obtained. However there was reasonable agreement with respect to a baseline illness rate that existed. This demonstrates that useful information may be obtained in this manner, although it should be supplemented with other data (e.g. serology) for a precise assessment of dynamics of disease occurrence during waterborne epidemic conditions.

scholarly journals Transient Dynamics in the Random Growth and Reset Model

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 306
Author(s):  
Tamás S. Biró ◽  
Lehel Csillag ◽  
Zoltán Néda
Keyword(s):  
Differential Equation ◽  
Mean Field ◽  
Equation System ◽  
Transient Dynamics ◽  
Type Model ◽  
Discrete Version ◽  
Differential Equation System ◽  
Practical Applications ◽  
Random Growth ◽  
Recursive Integration

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.

Estimating time to onset of swine influenza symptoms after initial novel A(H1N1v) viral infection

2010 ◽  
Vol 139 (9) ◽  
pp. 1418-1424 ◽  
Author(s):  
B. D. M. TOM ◽  
A. J. VAN HOEK ◽  
R. PEBODY ◽  
J. McMENAMIN ◽  
C. ROBERTSON ◽  
...  
Keyword(s):  
Incubation Time ◽  
Time Distribution ◽  
Age Groups ◽  
Swine Influenza ◽  
Interval Censoring ◽  
Limited Data ◽  
History Of ◽  
Influenza Case ◽  
Time To Onset

SUMMARYCharacterization of the incubation time from infection to onset is important for understanding the natural history of infectious diseases. Attempts to estimate the incubation time distribution for novel A(H1N1v) have been, up to now, based on limited data or peculiar samples. We characterized this distribution for a generic group of symptomatic cases using laboratory-confirmed swine influenza case-information. Estimates of the incubation distribution for the pandemic influenza were derived through parametric time-to-event analyses of data on onset of symptoms and exposure dates, accounting for interval censoring. We estimated a mean of about 1·6–1·7 days with a standard deviation of 2 days for the incubation time distribution in those who became symptomatic after infection with the A(H1N1v) virus strain. Separate analyses for the <15 years and ⩾15 years age groups showed a significant (P<0·02) difference with a longer mean incubation time in the older age group.

scholarly journals Kestabilan Model Epidemi SEIR Dengan Laju Insidensi

2015 ◽  
Vol 10 (2) ◽  
pp. 74
Author(s):  
Roni Tri Putra ◽  
Sukatik - ◽  
Sri Nita
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Equation System ◽  
Differential Equation System ◽  
Equilibrium Existence

In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with incidence rate. From the model it will be found investigated the existence and uniqueness solution  of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue. 

scholarly journals An accelerated differential equation system for generalized equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Qiyuan Wei ◽  
Liwei Zhang
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Maximal Monotone ◽  
Equation System ◽  
Generalized Equation ◽  
Generalized Equations ◽  
Differential Equation System ◽  
Step Size ◽  
Yosida Regularization ◽  
Numerical Discretization

<p style='text-indent:20px;'>An accelerated differential equation system with Yosida regularization and its numerical discretized scheme, for solving solutions to a generalized equation, are investigated. Given a maximal monotone operator <inline-formula><tex-math id="M1">\begin{document}$ T $\end{document}</tex-math></inline-formula> on a Hilbert space, this paper will study the asymptotic behavior of the solution trajectories of the differential equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation} \dot{x}(t)+T_{\lambda(t)}(x(t)-\alpha(t)T_{\lambda(t)}(x(t))) = 0,\quad t\geq t_0\geq 0, \end{equation} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>to the solution set <inline-formula><tex-math id="M2">\begin{document}$ T^{-1}(0) $\end{document}</tex-math></inline-formula> of a generalized equation <inline-formula><tex-math id="M3">\begin{document}$ 0 \in T(x) $\end{document}</tex-math></inline-formula>. With smart choices of parameters <inline-formula><tex-math id="M4">\begin{document}$ \lambda(t) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ \alpha(t) $\end{document}</tex-math></inline-formula>, we prove the weak convergence of the trajectory to some point of <inline-formula><tex-math id="M6">\begin{document}$ T^{-1}(0) $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M7">\begin{document}$ \|\dot{x}(t)\|\leq {\rm O}(1/t) $\end{document}</tex-math></inline-formula> as <inline-formula><tex-math id="M8">\begin{document}$ t\rightarrow +\infty $\end{document}</tex-math></inline-formula>. Interestingly, under the upper Lipshitzian condition, strong convergence and faster convergence can be obtained. For numerical discretization of the system, the uniform convergence of the Euler approximate trajectory <inline-formula><tex-math id="M9">\begin{document}$ x^{h}(t) \rightarrow x(t) $\end{document}</tex-math></inline-formula> on interval <inline-formula><tex-math id="M10">\begin{document}$ [0,+\infty) $\end{document}</tex-math></inline-formula> is demonstrated when the step size <inline-formula><tex-math id="M11">\begin{document}$ h \rightarrow 0 $\end{document}</tex-math></inline-formula>.</p>

scholarly journals Theoretical Vibration Analysis Regarding Excitation due to Elliptical Shaft Journals in Sleeve Bearings of Electrical Motors

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Ulrich Werner
Keyword(s):  
Differential Equation ◽  
Mathematical Description ◽  
Vibration Analysis ◽  
Equation System ◽  
Electrical Machines ◽  
Differential Equation System ◽  
Kinematic Constraints ◽  
Linear Differential ◽  
Electrical Motors ◽  
Rotor Mass

This paper shows a theoretical vibration analysis regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors, based on a simplified rotordynamic model. It is shown that elliptical shaft journals lead to kinematic constraints regarding the movement of the shaft journals on the oil film of the sleeve bearings and therefore to an excitation of the rotordynamic system. The solution of the linear differential equation system leads to the mathematical description of the movement of the rotor mass, the shaft journals, and the sleeve bearing housings. Additionally the relative movements between the shaft journals and the bearing housings are deduced, as well as the bearing housing vibration velocities. The presented simplified rotordynamic model can also be applied to rotating machines, other than electrical machines. In this case, only the electromagnetic spring valuecmhas to be put to zero.

scholarly journals Estimating the Force of Infection with Helicobacter pylori in Japan

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Taishi Kayano ◽  
Ki-Deok Lee ◽  
Hiroshi Nishiura
Keyword(s):  
Gastric Cancer ◽  
Helicobacter Pylori ◽  
World War Ii ◽  
Time Course ◽  
Force Of Infection ◽  
Seroprevalence Data ◽  
Age Dependent ◽  
The Future ◽  
Parameterized Model ◽  
H Pylori

Background. Although the seroprevalence against Helicobacter pylori (H. pylori) in Japan has declined over the birth year, Japanese people have yet exhibited a relatively high risk of gastric cancer. The present study employed mathematical models to estimate the time- and age-dependent force of infection with H. pylori in Japan, predicting the future seroprevalence by time and age. Methods. We investigated the published seroprevalence data against H. pylori in Japan from 1980–2018. Solving the McKendrick partial differential equation model, the seroprevalence was modeled as a function of survey year and age. Maximum likelihood estimation was conducted to estimate parameters governing the time- and age-dependent force of infection. Results. Among all fitted models, the time-dependent and age-independent model with an exponentially decaying force of infection over years was most favored. Fitted models indicated that the force of infection started to decrease during and/or shortly after the World War II. Using the parameterized model, the predicted fraction seropositive at the age of 40 years in 2018 was 0.22, but it is expected to decrease to 0.13 in 2030 and 0.05 in 2050, respectively. Conclusion. The time dependence was consistent with the decline in the force of infection as a function of the birth year. The force of infection has continuously and greatly declined over time, implying the diminished transmission of H. pylori through the time course and small chance of persistence. These findings are critical to anticipate the future decline in gastric cancer incidence.

OPTIMAL CONTROL FOR A NONLINEAR n-DIMENSIONAL COMPETING SYSTEM WITH AGE-STRUCTURE

2012 ◽  
Vol 05 (03) ◽  
pp. 1260008 ◽  
Author(s):  
ZHI-XUE LUO ◽  
JIAN-YU YANG ◽  
YA-JUAN LUO
Keyword(s):  
Optimal Control ◽  
Age Structure ◽  
Normal Cone ◽  
Equation System ◽  
Optimal Harvesting ◽  
Order Partial Differential Equation ◽  
Differential Equation System ◽  
Optimal Control Strategy ◽  
First Order

This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland's variational principle, the existence and unique characterization of the optimal control strategy are established. The optimality conditions for the control problem are obtained by the concept of the normal cone.

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