MATHEMATICAL MODELING AND ANALYSIS OF THE SPREAD OF CARRIER DEPENDENT INFECTIOUS DISEASES: EFFECTS OF CUMULATIVE DENSITY OF ENVIRONMENTAL FACTORS

2009 ◽  
Vol 02 (02) ◽  
pp. 213-228 ◽  
Author(s):  
SHIKHA SINGH ◽  
J. B. SHUKLA ◽  
PEEYUSH CHANDRA
Keyword(s):  
Environmental Factors ◽  
Infectious Diseases ◽  
Logistic Model ◽  
Cumulative Effect ◽  
Population Increase ◽  
Growth Equation ◽  
Nonlinear Mathematical Model ◽  
Modeling And Analysis ◽  
Dependent Growth ◽  
Carrier Population

In this paper, a nonlinear mathematical model with immigration for carrier dependent infectious diseases is proposed and analyzed by considering explicitly the cumulative effect of environmental factors, which are conducive to the growth of carrier population. It is assumed that the density of carrier population is governed by a general logistic model. It is assumed further that the growth rate per capita and the modified carrying capacity of carrier population increase as the cumulative density of environmental factors, governed by population density dependent growth equation, increases. It is shown that as the parameters governing environmental factors increase, the number of infectives in the population increases. It is also found that due to immigration, the disease becomes more endemic.

Modeling and Analysis of the Spread of Carrier Dependent Infectious Diseases with Environmental Effects

2003 ◽  
Vol 11 (03) ◽  
pp. 325-335 ◽  
Author(s):  
Shikha Singh ◽  
Peeyush Chandra ◽  
J. B. Shukla
Keyword(s):  
Population Density ◽  
Infectious Diseases ◽  
Logistic Model ◽  
Human Population ◽  
Population Increase ◽  
Related Factors ◽  
Modeling And Analysis ◽  
Modeling Process ◽  
Per Capita ◽  
Carrier Population

In this paper, SIS and SIRS models for carrier dependent infectious diseases with immigration are proposed and analyzed by considering effects of environmental and human population related factors which are conducive to the growth of carrier population. In the modeling process, the density of carrier population is governed by a general logistic model. Further, it is assumed that the growth rate per capita and the modified carrying capacity of carrier population increase as the human population density increases. In each case, it is shown that the spread of an infectious disease increases as the carrier population density increases and the disease becomes more endemic due to immigration.

scholarly journals Analysis of a Vaccination Model for Carrier Dependent Infectious Diseases with Environmental Effects

2008 ◽  
Vol 13 (3) ◽  
pp. 331-350 ◽  
Author(s):  
Ram Naresh ◽  
Surabhi Pandey ◽  
A. K. Misra
Keyword(s):  
Infectious Diseases ◽  
Logistic Model ◽  
Reproduction Number ◽  
Size Structure ◽  
Backward Bifurcation ◽  
Threshold Condition ◽  
Nonlinear Mathematical Model ◽  
Variable Size ◽  
Carrier Population

We have proposed and analyzed a nonlinear mathematical model for the spread of carrier dependent infectious diseases in a population with variable size structure including the role of vaccination. It is assumed that the susceptibles become infected by direct contact with infectives and/or by the carrier population present in the environment. The density of carrier population is assumed to be governed by a generalized logistic model and is dependent on environmental and human factors which are conducive to the growth of carrier population. The model is analyzed using stability theory of differential equations and numerical simulation. We have found a threshold condition, in terms of vaccine induced reproduction number R(φ) which is, if less than one, the disease dies out in the absence of carriers provided the vaccine efficacy is high enough, and otherwise the infection is maintained in the population. The model also exhibits backward bifurcation at R(φ) = 1. It is also shown that the spread of an infectious disease increases as the carrier population density increases. In addition, the constant immigration of susceptibles makes the disease more endemic.

scholarly journals Outstanding performance of an invasive alien tree Bischofia javanica relative to native tree species and implications for management of insular primary forests

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9573
Author(s):  
Tetsuto Abe ◽  
Nobuyuki Tanaka ◽  
Yoshikazu Shimizu
Keyword(s):  
Tree Species ◽  
Logistic Model ◽  
Forest Community ◽  
Population Increase ◽  
Canopy Trees ◽  
Native Trees ◽  
Native Tree ◽  
Native Tree Species ◽  
Bischofia Javanica ◽  
Primary Forests

Invasive alien tree species can exert severe impacts, especially in insular biodiversity hotspots, but have been inadequately studied. Knowledge of the life history and population trends of an invasive alien tree species is essential for appropriate ecosystem management. The invasive tree Bischofia javanica has overwhelmed native trees on Haha-jima Island in the Ogasawara Islands, Japan. We explored forest community dynamics 2 years after a typhoon damaged the Sekimon primary forests on Haha-jima Island, and predicted the rate of population increase of B. javanica using a logistic model from forest dynamics data for 19 years. During the 2 years after the typhoon, only B. javanica increased in population size, whereas populations of native tree species decreased. Stem diameter growth of B. javanica was more rapid than that of other tree species, including native pioneer trees. Among the understory stems below canopy trees of other species, B. javanica grew most rapidly and B. javanica canopy trees decreased growth of the dominant native Ardisia sieboldii. These competitive advantages were indicated to be the main mechanism by which B. javanica replaces native trees. The logistic model predicted that B. javanica would reach 30% of the total basal area between 2017 (in the eastern plot adjacent to a former B. javanica plantation) and 2057 (in the western plot distant from the plantation site), which is a maximum percentage allowing to eradicate under the present guideline of the National Forest. The results suggest immediate removal of B. javanica is required to preserve native biodiversity in these forests.

scholarly journals The impact of temperature and absolute humidity on the coronavirus disease 2019 (COVID-19) outbreak - evidence from China

2020 ◽  
Author(s):  
Peng Shi ◽  
Yinqiao Dong ◽  
Huanchang Yan ◽  
Xiaoyang Li ◽  
Chenkai Zhao ◽  
...  
Keyword(s):  
Environmental Factors ◽  
Infectious Diseases ◽  
Transmission Rate ◽  
Mainland China ◽  
Weather Condition ◽  
Absolute Humidity ◽  
List Type ◽  
Seir Model ◽  
Provincial Level ◽  
The Impact

ABSTRACTOBJECTIVETo investigate the impact of temperature and absolute humidity on the coronavirus disease 2019 (COVID-19) outbreak.DESIGNEcological study.SETTING31 provincial-level regions in mainland China.MAIN OUTCOME MEASURESData on COVID-19 incidence and climate between Jan 20 and Feb 29, 2020.RESULTSThe number of new confirm COVID-19 cases in mainland China peaked on Feb 1, 2020. COVID-19 daily incidence were lowest at -10 °C and highest at 10 °C, while the maximum incidence was observed at the absolute humidity of approximately 7 g/m3. COVID-19 incidence changed with temperature as daily incidence decreased when the temperature rose. No significant association between COVID-19 incidence and absolute humidity was observed in distributed lag nonlinear models. Additionally, A modified susceptible-exposed-infectious-recovered (M-SEIR) model confirmed that transmission rate decreased with the increase of temperature, leading to further decrease of infection rate and outbreak scale.CONCLUSIONTemperature is an environmental driver of the COVID-19 outbreak in China. Lower and higher temperatures might be positive to decrease the COVID-19 incidence. M-SEIR models help to better evaluate environmental and social impacts on COVID-19.What is already known on this topicMany infectious diseases present an environmental pattern in their incidence.Environmental factors, such as climate and weather condition, could drive the space and time correlations of infectious diseases, including influenza.Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) can be transmitted through aerosols, large droplets, or direct contact with secretions (or fomites) as influenza virus can.Little is known about environmental pattern in COVID-19 incidence.What this study addsThe significant association between COVID-19 daily incidence and temperature was confirmed, using 3 methods, based on the data on COVID-19 and weather from 31 provincial-level regions in mainland China.Environmental factors were considered on the basis of SEIR model, and a modified susceptible-exposed-infectious-recovered (M-SEIR) model was developed.Simulations of the COVID-19 outbreak in Wuhan presented similar effects of temperature on incidence as the incidence decrease with the increase of temperature.

scholarly journals Psi-Caputo Logistic Population Growth Model

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Muath Awadalla ◽  
Yves Yannick Yameni Noupoue ◽  
Kinda Abu Asbeh
Keyword(s):  
Population Growth ◽  
Fractional Derivative ◽  
Carrying Capacity ◽  
Chinese Population ◽  
Logistic Model ◽  
Logistic Equation ◽  
Logistic Growth ◽  
Growth Equation ◽  
Uniqueness Of The Solution ◽  
Better Than

This article studies modeling of a population growth by logistic equation when the population carrying capacity K tends to infinity. Results are obtained using fractional calculus theories. A fractional derivative known as psi-Caputo plays a substantial role in the study. We proved existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. The Chinese population, whose carrying capacity, K, tends to infinity, is used as evidence to prove that the proposed approach is appropriate and performs better than the usual logistic growth equation for a population with a large carrying capacity. A psi-Caputo logistic model with the kernel function x + 1 performed the best as it minimized the error rate to 3.20% with a fractional order of derivative α  = 1.6455.

Modeling and Analysis on the Rotation Accuracy of Lathe Spindle

2012 ◽  
Vol 602-604 ◽  
pp. 1757-1760
Author(s):  
Qiang Huang ◽  
Kun Wei
Keyword(s):  
Influence Factors ◽  
Cumulative Effect ◽  
Structure Characteristic ◽  
Analysis Method ◽  
Error Sources ◽  
Modeling And Analysis ◽  
Spindle Rotation ◽  
Machine Spindle ◽  
Center Track ◽  
The Impact

The rotation accuracy of the machine spindle is an important accuracy index, and has numerous influence factors. According to the structure characteristic of the spindle system, an integrated model of the spindle rotation error is established in this paper. By this model, the impact law and cumulative effect of various error sources on spindle rotation accuracy can be analyzed. Taking the lathe spindles as an example, the modeling and analysis method for spindle error are introduced. Visualization of spindle center track is achieved by programming.

scholarly journals Edward Harrison (1759–1838): An overlooked advocate of EcoHealth and One Health in the early 19th century

2020 ◽  
pp. 096777202092166
Author(s):  
Neil J Morley
Keyword(s):  
Environmental Factors ◽  
Infectious Diseases ◽  
19Th Century ◽  
Comparative Research ◽  
One Health ◽  
Spinal Deformities ◽  
Early 19Th Century ◽  
Veterinary Importance

Edward Harrison (1759–1838) was an English doctor best known for his ground-breaking treatments of spinal deformities and his failed attempts at medical reforms in the early 19th century. However, with the encouragement of his patient and patron Sir Joseph Banks, he also undertook comparative research on the influence of environmental factors on infectious diseases of medical and veterinary importance using approaches that were forerunners of the modern-day concepts of EcoHealth and One Health. His works in this field, particularly his study of sheep rot, are highlighted.

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