scholarly journals Subthreshold domain of bistable equilibria for a model of HIV epidemiology

2003 ◽  
Vol 2003 (58) ◽  
pp. 3679-3698 ◽  
Author(s):  
B. D. Corbett ◽  
S. M. Moghadas ◽  
A. B. Gumel
Keyword(s):  
Hiv Transmission ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Stability Analysis ◽  
Hiv Epidemiology ◽  
Preventive Vaccine ◽  
Hiv Eradication ◽  
Stable Equilibria ◽  
Multiple Stable Equilibria ◽  
Anti Hiv

A homogeneous-mixing population model for HIV transmission, which incorporates an anti-HIV preventive vaccine, is studied qualitatively. The local and global stability analysis of the associated equilibria of the model reveals that the model can have multiple stable equilibria simultaneously. The epidemiological consequence of this (bistability) phenomenon is that the disease may still persist in the community even when the classical requirement of the basic reproductive number of infection (ℛ0) being less than unity is satisfied. It is shown that under specific conditions, the community-wide eradication of HIV is feasible ifℛ0<ℛ∗, whereℛ∗is some threshold quantity less than unity. Furthermore, for the bistability case (which occurs whenℛ∗<ℛ0<1), it is shown that HIV eradication is dependent on the initial sizes of the subpopulations of the model.

EXOGENOUS REINFECTION AND RESURGENCE OF TUBERCULOSIS: A THEORETICAL FRAMEWORK

2004 ◽  
Vol 12 (02) ◽  
pp. 231-247 ◽  
Author(s):  
S. M. MOGHADAS ◽  
M. E. ALEXANDER
Keyword(s):  
Multiple Equilibria ◽  
Incidence Rates ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
High Prevalence ◽  
Saturated Incidence ◽  
Stable Equilibria ◽  
Parameter Values ◽  
Multiple Stable Equilibria ◽  
Exogenous Reinfection

The importance of exogenous reinfection versus endogenous reactivation for the resurgence of tuberculosis (TB) has been a matter of ongoing debate. Previous mathematical models of TB give conflicting results on the possibility of multiple stable equilibria in the presence of reinfection, and hence the failure to control the disease even when the basic reproductive number is less than unity. The present study reconsiders the effect of exogenous reinfection, by extending previous studies to incorporate a generalized rate of reinfection as a function of the number of actively infected individuals. A mathematical model is developed to include all possible routes to the development of active TB (progressive primary infection, endogenous reactivation, and exogenous reinfection). The model is qualitatively analyzed to show the existence of multiple equilibria under realistic assumptions and plausible range of parameter values. Two examples, of unbounded and saturated incidence rates of reinfection, are given, and simulation results using estimated parameter values are presented. The results reflect exogenous reinfection as a major cause of TB emergence, especially in high prevalence areas, with important public health implications for controlling its spread.

scholarly journals A Mathematical Model of HIV Transmission in Homosexuals with Genetic Heterogeneity

2000 ◽  
Vol 2 (4) ◽  
pp. 285-296 ◽  
Author(s):  
Shu-Fang Hsu Schmtiz
Keyword(s):  
Hiv Infection ◽  
San Francisco ◽  
Hiv Transmission ◽  
Natural Resistance ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Limited Data ◽  
Multiple Exposures ◽  
The Impact ◽  
Mutant Genes

Several AIDS cohort studies observe that the incubation period between HIV infection and AIDS onset can be shorter than 3 years in about 10% seropositive individuals, or longer than 10 years in about 10-15% individuals. On the other hand, many individuals remain seronegative even after multiple exposures to HIV. These distinct outcomes have recently been correlated with some mutant genes in HIV co-receptors (e.g., CCR5,CCR2 and CXCR4). For instance, the mutant alleles △32 and m303 of CCR5 may provide full protection against HIV infection in homozygotes and partial protection in heterozygotes; moreover, infected heterozygotes may progress more slowly than individuals who have no mutant alleles. Frequencies of these mutant alleles are not very low in Caucasian populations, therefore, their effects may not be insignificant. Based on available data, we propose a one-sex model with susceptibles classified as having no, partial or full natural resistance to HIV infection, and infecteds classified as rapid, normal or slow progressors. Our goals are to investigate the impact of such heterogeneity on the spread of HIV and to identify key parameters. The basic reproductive numberR0is derived from a simplified model. The relative contributions toR0from the three groups of infecteds are investigated. We present a rough estimating procedure making use of limited data to estimate some new parameters specific to our model. Finally the rough estimating procedure is applied to an example focusing on CCR5-△32 in San Francisco gay men. The relative contributions toR0among the three infected groups are compared using two different classifying criteria for infecteds. Under given assumptions, we conclude that, without any intervention, HIV infection will continue to spread in this population and the epidemic is mainly driven by the normal progressors. The transmission rates from infecteds are identified as key parameters.

scholarly journals Assessing the danger of self-sustained HIV epidemics in heterosexuals by population based phylogenetic cluster analysis

eLife ◽  
2017 ◽  
Vol 6 ◽  
Author(s):  
Teja Turk ◽  
Nadine Bachmann ◽  
Claus Kadelka ◽  
Jürg Böni ◽  
Sabine Yerly ◽  
...  
Keyword(s):  
Process Model ◽  
Hiv Transmission ◽  
Sequence Data ◽  
Population Based ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Epidemic Threshold ◽  
Transmission Parameters ◽  
Phylogenetic Cluster ◽  
Potential Factors

Assessing the danger of transition of HIV transmission from a concentrated to a generalized epidemic is of major importance for public health. In this study, we develop a phylogeny-based statistical approach to address this question. As a case study, we use this to investigate the trends and determinants of HIV transmission among Swiss heterosexuals. We extract the corresponding transmission clusters from a phylogenetic tree. To capture the incomplete sampling, the delayed introduction of imported infections to Switzerland, and potential factors associated with basic reproductive number R0, we extend the branching process model to infer transmission parameters. Overall, the R0 is estimated to be 0.44 (95%-confidence interval 0.42—0.46) and it is decreasing by 11% per 10 years (4%—17%). Our findings indicate rather diminishing HIV transmission among Swiss heterosexuals far below the epidemic threshold. Generally, our approach allows to assess the danger of self-sustained epidemics from any viral sequence data.

scholarly journals Dynamics analysis of an online gambling spreading model on scale-free networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yu Kong ◽  
Tao Li ◽  
Yuanmei Wang ◽  
Xinming Cheng ◽  
He Wang ◽  
...  
Keyword(s):  
Network Topology ◽  
Negative Impact ◽  
Online Gambling ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Scale Free ◽  
Spreading Model ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
Gambling Policy

AbstractNowadays, online gambling has a great negative impact on the society. In order to study the effect of people’s psychological factors, anti-gambling policy, and social network topology on online gambling dynamics, a new SHGD (susceptible–hesitator–gambler–disclaimer) online gambling spreading model is proposed on scale-free networks. The spreading dynamics of online gambling is studied. The basic reproductive number $R_{0}$ R 0 is got and analyzed. The basic reproductive number $R_{0}$ R 0 is related to anti-gambling policy and the network topology. Then, gambling-free equilibrium $E_{0}$ E 0 and gambling-prevailing equilibrium $E_{ +} $ E + are obtained. The global stability of $E_{0}$ E 0 is analyzed. The global attractivity of $E_{ +} $ E + and the persistence of online gambling phenomenon are studied. Finally, the theoretical results are verified by some simulations.

scholarly journals Effects of social distancing on the spreading of COVID-19 inferred from mobile phone data

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hamid Khataee ◽  
Istvan Scheuring ◽  
Andras Czirok ◽  
Zoltan Neufeld
Keyword(s):  
Mobile Phone ◽  
Basic Reproductive Number ◽  
Mobile Phone Data ◽  
Reproductive Number ◽  
Expansion Phase ◽  
Social Distancing ◽  
Exponential Expansion ◽  
Total Death ◽  
Mobility Reduction ◽  
Epidemiological Parameters

AbstractA better understanding of how the COVID-19 pandemic responds to social distancing efforts is required for the control of future outbreaks and to calibrate partial lock-downs. We present quantitative relationships between key parameters characterizing the COVID-19 epidemiology and social distancing efforts of nine selected European countries. Epidemiological parameters were extracted from the number of daily deaths data, while mitigation efforts are estimated from mobile phone tracking data. The decrease of the basic reproductive number ($$R_0$$ R 0 ) as well as the duration of the initial exponential expansion phase of the epidemic strongly correlates with the magnitude of mobility reduction. Utilizing these relationships we decipher the relative impact of the timing and the extent of social distancing on the total death burden of the pandemic.

scholarly journals Huanglongbing Model under the Control Strategy of Discontinuous Removal of Infected Trees

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1164
Author(s):  
Weiwei Ling ◽  
Pinxia Wu ◽  
Xiumei Li ◽  
Liangjin Xie
Keyword(s):  
Infectious Disease ◽  
Global Stability ◽  
Control Strategy ◽  
Theoretical Basis ◽  
Dynamic Properties ◽  
Transmission Mechanism ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Vector Borne ◽  
Citrus Trees

By using differential equations with discontinuous right-hand sides, a dynamic model for vector-borne infectious disease under the discontinuous removal of infected trees was established after understanding the transmission mechanism of Huanglongbing (HLB) disease in citrus trees. Through calculation, the basic reproductive number of the model can be attained and the properties of the model are discussed. On this basis, the existence and global stability of the calculated equilibria are verified. Moreover, it was found that different I0 in the control strategy cannot change the dynamic properties of HLB disease. However, the lower the value of I0, the fewer HLB-infected citrus trees, which provides a theoretical basis for controlling HLB disease and reducing expenditure.

scholarly journals Design and Optimal Control of a Multistable, Cooperative Microactuator

Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 183
Author(s):  
Michael Olbrich ◽  
Arwed Schütz ◽  
Tamara Bechtold ◽  
Christoph Ament
Keyword(s):  
Deflection Angle ◽  
Initial State ◽  
New Concepts ◽  
Vertical Displacements ◽  
State Uncertainty ◽  
Stable Equilibria ◽  
Freely Moving ◽  
Time And Energy ◽  
Multiple Stable Equilibria ◽  
Optimal Trajectory Planning

In order to satisfy the demand for the high functionality of future microdevices, research on new concepts for multistable microactuators with enlarged working ranges becomes increasingly important. A challenge for the design of such actuators lies in overcoming the mechanical connections of the moved object, which limit its deflection angle or traveling distance. Although numerous approaches have already been proposed to solve this issue, only a few have considered multiple asymptotically stable resting positions. In order to fill this gap, we present a microactuator that allows large vertical displacements of a freely moving permanent magnet on a millimeter-scale. Multiple stable equilibria are generated at predefined positions by superimposing permanent magnetic fields, thus removing the need for constant energy input. In order to achieve fast object movements with low solenoid currents, we apply a combination of piezoelectric and electromagnetic actuation, which work as cooperative manipulators. Optimal trajectory planning and flatness-based control ensure time- and energy-efficient motion while being able to compensate for disturbances. We demonstrate the advantage of the proposed actuator in terms of its expandability and show the effectiveness of the controller with regard to the initial state uncertainty.

scholarly journals Effect of specific non-pharmaceutical intervention policies on SARS-CoV-2 transmission in the counties of the United States

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Bingyi Yang ◽  
Angkana T. Huang ◽  
Bernardo Garcia-Carreras ◽  
William E. Hart ◽  
Andrea Staid ◽  
...  
Keyword(s):  
United States ◽  
Home Visiting ◽  
Leisure Activities ◽  
The United States ◽  
Causal Effects ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
County Level ◽  
Metapopulation Model ◽  
Pharmaceutical Interventions

AbstractNon-pharmaceutical interventions (NPIs) remain the only widely available tool for controlling the ongoing SARS-CoV-2 pandemic. We estimated weekly values of the effective basic reproductive number (Reff) using a mechanistic metapopulation model and associated these with county-level characteristics and NPIs in the United States (US). Interventions that included school and leisure activities closure and nursing home visiting bans were all associated with a median Reff below 1 when combined with either stay at home orders (median Reff 0.97, 95% confidence interval (CI) 0.58–1.39) or face masks (median Reff 0.97, 95% CI 0.58–1.39). While direct causal effects of interventions remain unclear, our results suggest that relaxation of some NPIs will need to be counterbalanced by continuation and/or implementation of others.

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