A Susceptible-Infectious (SI) model with two infective stages and an endemic equilibrium

Author(s):  
Semra Ahmetolan ◽  
Ayse Humeyra Bilge ◽  
Ali Demirci ◽  
Ayse Peker Dobie
Keyword(s):  
2020 ◽  
Vol 53 (2) ◽  
pp. 2576-2581
Author(s):  
Fangzhou Liu ◽  
Shaoxuan CUI ◽  
Xianwei Li ◽  
Martin Buss

Forests ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 209
Author(s):  
Luiza Tymińska-Czabańska ◽  
Jarosław Socha ◽  
Marek Maj ◽  
Dominika Cywicka ◽  
Xo Viet Hoang Duong

Site productivity provides critical information for forest management practices and is a fundamental measure in forestry. It is determined using site index (SI) models, which are developed using two primary groups of methods, namely, phytocentric (plant-based) or geocentric (earth-based). Geocentric methods allow for direct site growth modelling, in which the SI is predicted using multiple environmental indicators. However, changes in non-static site factors—particularly nitrogen deposition and rising CO2 concentration—lead to an increase in site productivity, which may be visible as an age trend in the SI. In this study, we developed a geocentric SI model for oak. For the development of the SI model, we used data from 150 sample plots, representing a wide range of local topographic and site conditions. A generalized additive model was used to model site productivity. We found that the oak SI depended predominantly on physicochemical soil properties—mainly nitrogen, carbon, sand, and clay content. Additionally, the oak SI value was found to be slightly shaped by the topography, especially by altitude above sea level, and topographic position. We also detected a significant relationship between the SI and the age of oak stands, indicating the long-term increasing site productivity for oak, most likely caused by nitrogen deposition and changes in climatic conditions. The developed geocentric site productivity model for oak explained 77.2% of the SI variation.


2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yakui Xue ◽  
Tiantian Li

We study a delayed SIR epidemic model and get the threshold value which determines the global dynamics and outcome of the disease. First of all, for anyτ, we show that the disease-free equilibrium is globally asymptotically stable; whenR0<1, the disease will die out. Directly afterwards, we prove that the endemic equilibrium is locally asymptotically stable for anyτ=0; whenR0>1, the disease will persist. However, for anyτ≠0, the existence conditions for Hopf bifurcations at the endemic equilibrium are obtained. Besides, we compare the delayed SIR epidemic model with nonlinear incidence rate to the one with bilinear incidence rate. At last, numerical simulations are performed to illustrate and verify the conclusions.


2021 ◽  
pp. 1-12
Author(s):  
LIU YANG ◽  
YUKIHIKO NAKATA

For some diseases, it is recognized that immunity acquired by natural infection and vaccination subsequently wanes. As such, immunity provides temporal protection to recovered individuals from an infection. An immune period is extended owing to boosting of immunity by asymptomatic re-exposure to an infection. An individual’s immune status plays an important role in the spread of infectious diseases at the population level. We study an age-dependent epidemic model formulated as a nonlinear version of the Aron epidemic model, which incorporates boosting of immunity by a system of delay equations and study the existence of an endemic equilibrium to observe whether boosting of immunity changes the qualitative property of the existence of the equilibrium. We establish a sufficient condition related to the strength of disease transmission from subclinical and clinical infective populations, for the unique existence of an endemic equilibrium.


Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.


2017 ◽  
Vol 13 (7) ◽  
pp. 69
Author(s):  
Pasit Leeniva ◽  
Prapatpong Upala

The objectives of this research are to evaluate acoustic environments and to forecast STI values from spatial component variables in the large classrooms of the Thai public university that were specially controlled the same room finishing materials including the floor, walls, and ceiling. Whereas the five spatial component factors included (1) Room Volume (RV), (2) Ceiling Height (CH), (3) the Ratio of Depth to Width (Rdw), (4) Total Room Surface (TS), and (5) Percentage of Absorbing Surface areas (PAS). The research tools were the smartphones that used the applications for acoustical evaluation and speech intelligibility analysis. The Speech Transmission Index (STI), Reverberation Time (RT), and Background Noise Level (BNL) were collected by the calibrated microphone in the nine points distributed across the entire room. And also, the sounds for testing were simulated such as balloon burst, and STIPA signal via a sound generator. The Thailand Speech Intelligibility (T-SI) model was developed by the multiple regression analysis with a statistical at a confidence level of 95%.The results showed that this T-SI model depended on the strongly positive relationship of PAS and the slightly positive relationship of CH, TS while the RV, Rdw were slightly the negative relationship and which predicted STI values. Moreover, the highest affecting variable of T-SI model was CH and the lowest was PAS. However, this research implies that the improving room acoustic quality would be adjusting the sound absorbing surface areas i.e., increase the cloth curtain or appropriate methods.


2014 ◽  
Vol 46 (01) ◽  
pp. 241-255 ◽  
Author(s):  
Peter Neal

We study the endemic behaviour of a homogeneously mixing SIS epidemic in a population of size N with a general infectious period, Q, by introducing a novel subcritical branching process with immigration approximation. This provides a simple but useful approximation of the quasistationary distribution of the SIS epidemic for finite N and the asymptotic Gaussian limit for the endemic equilibrium as N → ∞. A surprising observation is that the quasistationary distribution of the SIS epidemic model depends on Q only through


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