A nonlinear AIDS epidemic model with screening and time delay

Naresh, Ram; Tripathi, Agraj; Sharma, Dileep

doi:10.1016/j.amc.2010.10.036

Cited by 25 publications

(15 citation statements)

References 25 publications

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“…This variable is usually the most important factor in predicting the number of infections and diseases [78,79]. However, this variable is especially important if there is a time lag between incidence and healthcare system response with possible consequences for virus spread dynamics in space [80,81].…”

Section: Plos Onementioning

confidence: 99%

The macroecology of the COVID-19 pandemic in the Anthropocene

et al. 2020

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Severe acute respiratory syndrome coronavirus 2, the virus that causes coronavirus disease 2019 (COVID-19), has expanded rapidly throughout the world. Thus, it is important to understand how global factors linked with the functioning of the Anthropocene are responsible for the COVID-19 outbreak. We tested hypotheses that the number of COVID-19 cases, number of deaths and growth rate of recorded infections: (1) are positively associated with population density as well as (2) proportion of the human population living in urban areas as a proxies of interpersonal contact rate, (3) age of the population in a given country as an indication of that population's susceptibility to COVID-19; (4) net migration rate and (5) number of tourists as proxies of infection pressure, and negatively associated with (5) gross domestic product which is a proxy of health care quality. Data at the country level were compiled from publicly available databases and analysed with gradient boosting regression trees after controlling for confounding factors (e.g. geographic location). We found a positive association between the number of COVID-19 cases in a given country and gross domestic product, number of tourists, and geographic longitude. The number of deaths was positively associated with gross domestic product, number of tourists in a country, and geographic longitude. The effects of gross domestic product and number of tourists were non-linear, with clear thresholds above which the number of COVID-19 cases and deaths increased rapidly. The growth rate of COVID-19 cases was positively linked to the number of tourists and gross domestic product. The growth rate of COVID-19 cases was negatively associated with the mean age of the population and geographic longitude. Growth was slower in less urbanised countries. This study demonstrates that the characteristics of the human population and high mobility, but not population density, may help explain the global spread of the virus. In addition, geography, possibly via climate, may play a role in the pandemic. The unexpected positive and strong association between gross domestic product and number of cases, deaths, and growth rate suggests that COVID-19 may be a new civilisation disease affecting rich economies.

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Section: Plos Onementioning

confidence: 99%

The macroecology of the COVID-19 pandemic in the Anthropocene

et al. 2020

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“…The time delay may influence the dynamics of infectious diseases. In fact, many diseases have different kinds of delays when they spread, such as immunity period delay [7,8], infection period delay [9], and incubation period delay [10][11][12][13][14]. It is well known that the dynamical behaviors (including stability, attractivity, persistence, periodic oscillation, bifurcation, and chaos) of population models with time delay have become a subject of intense research activities.…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period

Sirijampa

Chinviriyasit

2018

Adv Differ Equ

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In this paper, we analyze a delayed SEIR epidemic model in which the latent and infected states are infective. The model has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number R 0 , is less than or equal to unity. We investigate the effect of the time delay on the stability of endemic equilibrium when R 0 > 1. We give criteria that ensure that endemic equilibrium is asymptotically stable for all time delays and a Hopf bifurcation occurs as time delay exceeds the critical value. We give formulae for the direction of Hopf bifurcations and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold reduction for functional differential equations. Numerical simulations are presented to illustrate the analytical results.

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“…Mathematical studies can be effective as it guides to the evaluation, testing and implementation of strategies over short or long time scales for chronic relapsing diseases such as alcohol addiction, drug abuse etc. There are many mathematical models for epidemic diseases like HIV [4][5][6][7][8][9], SARS [10], gonorrhea [11,12], dengue [13], cancer [14][15][16], Chlamydia [17], HFMD [18][19][20][21] etc. But the mathematical models on alcohol and drug abuse are very small in number though they have been referred to in terms of epidemics.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a drinking epidemic model

Sharma

Samanta

2015

Int. J. Dynam. Control

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In this paper, we have developed a mathematical model of alcohol abuse which consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. We have discussed about basic properties of the system. Sensitivity analysis of the system is also discussed. Next, Basic reproduction number (R 0 ) is calculated. The stability analysis of the model shows that the system is locally asymptotically stable at disease free equilibrium E 0 when R 0 < 1. When R 0 > 1, endemic equilibrium E * exists and the system becomes locally asymptotically stable at E * and E 0 becomes unstable. We have also discussed the global stability of the system at E 0 . It is also found that a backward bifurcation may occur at R 0 = 1. Next we have discussed the drinking epidemic model with treatment control. An objective functional is considered which is based on a combination of minimizing the number of heavy drinkers and the cost of treatment. Then an optimal control is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB, which show the reliability of our model from the practical point of view. Epidemiological implications of our analytical findings are addressed critically.

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A nonlinear AIDS epidemic model with screening and time delay

Cited by 25 publications

References 25 publications

The macroecology of the COVID-19 pandemic in the Anthropocene

The macroecology of the COVID-19 pandemic in the Anthropocene

Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period

Analysis of a drinking epidemic model

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