Modeling and dynamics of HIV transmission among high-risk groups in Guangzhou city, China

In this paper, a multicompartmental model is formulated to study how HIV is transmitted among different HIV high-risk groups, including MSM (men who have sex with men), FRs (foreigner residents), FSWs (female sex workers), and IDUs (injection drug users). The explicit expression for the basic reproduction number is obtained via the next generation matrix approach. We show that the disease free equilibrium is locally as well as globally asymptotically stable (the disease goes to extinction) when the basic reproduction number is less than unity, and the disease is always present when the basic reproduction number is larger than unity. As an illustration of our theoretical results, we conduct numerical simulations. We also conduct a case study where model parameters are estimated from the demographic and epidemiological data from Guangzhou. Using the parameter estimates, we predict the HIV/AIDS trend for each high-risk group. Furthermore, our study suggests that reducing the transmission routes of the disease and increasing condom use will be useful for control of HIV transmission.     

A nested model on HIV/AIDs, antiretroviral therapy and drug resistance

A coupled within- (immunological) and between-host (epidemiological) dynamic model was developed which is about the spreading of drug-sensitive HIV strain and drug-resistant HIV strain in men who have sex with men (MSM) population. The within-host model was nested within the between-host model by linking the dynamics of the within-host model to the additional host mortality and transmission rate of the infection. The existences of equilibria and their stabilities were found, as well as the thresholds $\mathcal {R}_S$ and $\mathcal {R}_R$ for the two different strains of the nested model. Some simulations about the spreading of the two HIV strains in Beijing MSM population were given. Our results show that the drug-resistant strain will increase quite fast in this population and both strains can coexist, which will make a big pressure for China''s ``Four-Free-One-Care Policy''.     

Small world network models of the dynamics of HIV infection

It has long been recognised that the structure of social networks plays an important role in the dynamics of disease propagation. The spread of HIV results from a complex network of social interactions and other factors related to culture, sexual behaviour, demography, geography and disease characteristics, as well as the availability, accessibility and delivery of healthcare. The small world phenomenon has recently been used for representing social network interactions. It states that, given some random connections, the degrees of separation between any two individuals within a population can be very small. In this paper we present a discrete event simulation model which uses a variant of the small world network model to represent social interactions and the sexual transmission of HIV within a population. We use the model to demonstrate the importance of the choice of topology and initial distribution of infection, and capture the direct and non-linear relationship between the probability of a casual partnership (small world randomness parameter) and the spread of HIV. Finally, we illustrate the use of our model for the evaluation of interventions such as the promotion of safer sex and introduction of a vaccine.     

Global dynamics and cost-effectiveness analysis of HIV pre-exposure prophylaxis and structured treatment interruptions based on a multi-scale model

Structured treatment interruptions (STI) were proposed to reduce costs and side effects for HIV infected individuals, but whether the possible viral rebound within hosts after treatment interruption would lead to more new infections and additional costs among the population remains unknown. Oral pre-exposure prophylaxis (PrEP) is shown as an effective but expensive strategy to prevent the acquisition of HIV infection. To investigate the effectiveness and cost-effectiveness of STI and PrEP, we develop a multi-scale model linking within-host and between-host dynamics in the presence of drug resistance. Lyapunov functionals are constructed to analyze the global dynamics of the coupled system. We fit this model to the annual AIDS incidence and death data from 1980 to 2014 among men who have sex with men (MSM) in San Francisco and compare the impact of six various intervention scenarios (low, medium, high PrEP coverage with or without STI) on new infections and cost-effectiveness over the next 20 years. We estimate the PrEP efficacy needed to eliminate the disease for different fraction of acquired drug resistance under the above six scenarios. Numerical simulations show that expanding PrEP coverage is very cost-effective, but whether implementing STI is cost-saving depends on the efficacy of second-line drugs. That is to say, STI could always save money, but it may lead to more (less) new infections than continuous therapy and thus less (more) health benefit for high (low) efficacy of second-line drugs. These results provide insights about the long-term effect of STI and PrEP on the disease control and cost-effectiveness.     

The persistence of HIV-1 spreading in MSM population in China

In this work, we develop and analyze mathematical models for the dynamics about the evolution of HIV/AIDS in men who have sex with men in China. We focus on the analyses of the basic reproduction number $R_0$ and the persistence of infection. Through simulations we also find that the interventions including antiviral therapy, condom using and potential vaccinations play very important roles in the HIV/AIDS spreading in MSM population in China.     

一类非线性动力系统的数值分析及控制策略研究

根据艾滋病在新疆的流行特点,建立了一个非线性动力系统的数学模型来研究艾滋病在新疆高危人群中传播的规律.通过查阅大量的统计数据和文献资料,确定了模型中部分参数的具体数值,然后通过数据拟合的方法得到了各个高危人群中的HIV病毒的传染性系数.在模型中,选择2004年底(2005年初)作为系统的初始点,预测了艾滋病未来几年内在新疆的流行趋势.最后,提出并比较遏止艾滋病传播的各项干预措施.     

Modeling sexual transmission of HIV/AIDS in Jiangsu province,China

HIV transmission by sexual activities exhibits a substantial increase and has become a primary transmission mode in China recently. A mathematical model is formulated so as to identify the key processes and parameters that could explain the quick increase in the proportion of heterosexual transmission and further to assist in suggesting control measures urgently. On the basis of surveillance data on a number of people living with HIV/AIDS in Jiangsu province, we parameterize the model and estimate the reproduction number by using the least squares method. The basic reproduction number was estimated to be R₀ = 3.52 for the therapy scenario of heterosexual transmission. The model predicts that the epidemic will peak in 2020. New infections are sensitive to the transmission coefficient, dependent on condom use rate, and the risky activities during the early period, whereas are sensitive to the recruitment rate in the late period of the transmission respectively. Antiviral therapy can either increase or decrease the new infections depending on both the extended life span of treated individuals and the infectiousness of the treated individuals. Hence, effective control measures during different transmission periods can be suggested, and antiretroviral therapy is a contentious issue for disease control. Copyright © 2012 John Wiley & Sons, Ltd.     

A network modelling approach for assessing the efficiency of prevention strategies

Survey data and a simulation model based on a stochastic pair formation process are used to construct networks of sexual contacts. We model heterosexual partnerships which can be steady or casual depending on their average duration. Transmission of an infectious disease can take place in pairs of a susceptible and an infected individual. We study networks of sexual contacts accumulated during 1 year for different types of mixing patterns. The networks are constructed on the basis of data from a survey in The Netherlands. We analyze the network structure for different mixing patterns and investigate the relationship between network structure and disease spread; furthermore we study the effect of prevention measures on the structure of the network.     

具有商业性行为的女性吸毒者对HIV/AIDS传播的影响

利用数学模型,研究了具有商业性行为的女性吸毒者对HIV/AIDS传播的影响.通过理论分析,讨论了系统的一致持续性和地方病平衡点的存在性,从理论上揭示了女性吸毒者的商业性行为可加强HIV/AIDS的传播和流行.特别地,若无商业性行为且吸毒人群和一般男性人群中均无疾病流行时,商业性行为的存在将会导致两类人群中的疾病均流行起来.这为防控工作的开展提供了重要参考.     

A linked risk group model for investigating the spread of HIV

This paper describes a model that simulates the spread of HIV and progression to AIDS. The model is based on classical models of disease transmission. It consists of six linked risk groups and tracks the numbers of infectives, AIDS cases, AIDS related deaths, and other deaths of infected persons in each risk group. Parametric functions are used to represent risk-group-specific and time-dependent average contact rates. Contacts are needle sharing, sexual contacts, or blood product transfers.

An important feature of the model is that the contact rate parameters are estimated by minimizing differences between AIDS incidence and reported AIDS cases adjusted for undercounting biases. This feature results in an HIV epidemic curve that is analogous to one estimated by backcalculation models but whose dynamics are determined by simulating disease transmission. The model exhibits characteristics of both the disease transmission and the backcalculation approaches, i.e., the model:

• reconstructs the historical behavior patterns of the different risk groups,

• includes separate effects of treatment and changes in average contact rates,

• accounts for other mortality risks for persons infected with HIV,

• calculates short-term projections of AIDS incidence, HIV incidence, and HIV prevalence,

• calculates cumulative HIV infections (the quantity calculated by backcalculation approaches) and HIV prevalence (the quantity measured by seroprevalence and sentinel surveys). This latter feature permits the validation of the estimates generated by two distinct approaches.

We demonstrate the use of the model with an application to U.S. AIDS data through 1991.     

Dynamical analysis of public health education on HIV/AIDS transmission

An Human Immunodeficiency Virus/Acquired Immuno‐Deficiency Syndrome (HIV/AIDS) epidemic model for sexual transmission with asymptomatic and symptomatic phase is proposed as a system of differential equations. The threshold and steady state for the model are determined and stabilities of disease free steady state is investigated. We use the model and study the effect of public health education on the spread of HIV/AIDS as a single‐strategy in HIV prevention. The education, including basic reproduction number for the model with public health education, is compared with the basic reproduction number for the HIV/AIDS in the absence of public health education. By comparing these two values, influence of public health education appears. According to property of , threshold proportion of educated adolescents, education rate for susceptible individuals and education efficacy is obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal control and sensitivity analysis of SIV→HIV dynamics with effects of infected immigrants in sub‐Saharan Africa

Regional migration has become an underlying factor in the spread of HIV transmission. In addition, immigrants with HIV status has contributed with high‐risk of sexually transmitted infection to its “destination” communities and promotes dissemination of HIV. Efforts to address HIV/AIDS among conflict‐affected populations should be properly addressed to eliminate potential role of the spread of the disease and risk of exposure to HIV. Motivated from this situation, HIV‐infected immigrants factor to HIV/SIV transmission link will be investigated in this research and examine its potential effect using optimal control method. Nonlinear deterministic mathematical model is used which is a multiple host model comprising of humans and chimpanzees. Some basic properties of the model such as invariant region and positivity of the solutions will be examined. The local stability of the disease‐free equilibrium was examined by computing the basic reproduction number, and it was found to be locally asymptotically stable when ?₀<1 and unstable otherwise. Sensitivity analysis was conducted to determine the parameters that help most in the spread of the virus. Pontryagin's maximum principle is used to obtain the optimality conditions for controlling the disease spread. Numerical simulation was conducted to obtain the analytical results. The results shows that combination of public health awareness, treatment, and culling help in controlling the HIV disease spread.     

女性吸毒者在HIV/AIDS传播中的作用

利用数学模型,探讨了女性吸毒者在HIV/AIDS传播中的作用.通过理论分析和数值模拟,揭示了女性吸毒者对HIV/AIDS传播和流行的重要作用:当HIV/AIDS在吸毒人群和一般男性人群中流行时,若切断女性吸毒人群和一般男性人群间的传播途径(商业性行为),则疾病不但在一般男性人群中会消亡,在一定的条件下,甚至会在吸毒人群中消亡.     

Dynamics of an HIV‐1 virus model with both virus‐to‐cell and cell‐to‐cell transmissions,general incidence rate,intracellular delay,and CTL immune responses

Direct cell‐to‐cell transmission of HIV‐1 is a more efficient means of virus infection than virus‐to‐cell transmission. In this paper, we incorporate both these transmissions into an HIV‐1 virus model with nonlinear general incidence rate, intracellular delay, and cytotoxic T lymphocyte (CTL) immune responses. This model admits three types of equilibria: infection‐free equilibrium, CTL‐inactivated equilibrium, and CTL‐activated equilibrium. By using Lyapunov functionals and LaSalle invariance principle, it is verified that global threshold dynamics of the model can be explicitly described by the basic reproduction numbers.     

Quantifying the strength and durability of induced immunity to HIV infection in women engaging in unprotected sexual contacts with infected men

Evidence is accumulating that exposure to human immunodeficiency virus (HIV) can lead to an increased resistance or immunity to subsequent infection. A multirisk model that permits either induced immunity or infection to develop after heterosexual inoculation with HIV is shown to be compatible with a wide spectrum of disparate male-to-female transmission data.When the model is applied to time-dependent, HIV-seroprevalence data, the probability that an unexposed woman would remain unexposed after an unprotected contact with an infected man was estimated to be greater than 0.95 on the average. Thus, it would require at least 14 unprotected sexual contacts with HIV-infected men for 50% of an unexposed cohort of women to become exposed to the virus. This suggests that there is a low probability that HIV virions will be found to have penetrated the mucosal barriers of the reproductive tract after a contact.The model also predicts, that the average woman whose mucosal barriers have been breached by HIV has a significant probability of developing immunity to the virus rather than infection. Modelling data for a cohort of unexposed Nairobi women leads to the prediction that the probability of acquiring induced immunity per contact is about 60% of the probability of acquiring the disease per contact.The modelling results also predict that those who had developed resistance to HIV run the small, but significant risk of becoming infected nonetheless by continuing high-risk behavior. For the common contact rate of ten per month, the modelling predicts that the HIV-transmission risk per contact for unexposed women in the Nairobi cohort is 1/178 while the transmission risk for the cohort's immunized women is 1/1548. These numbers suggest that HIV infection is difficult to transmit through heterosexual intercourse on the average and that male-to-female HIV-transmission risk per contact for African women lies between 1/178 and 1/1548.Direct confirmation of the predictions in the last paragraph has been subsequently observed in two completely independent studies. The Nairobi research team recently reported that a notable number of Nairobi prostitutes previously identified to be members of the HIV-resistant group became infected nonetheless. Second, in a study of 174 sexually monogamous, discordant couples in Rakai, Uganda reporting contacts rates of nine to ten per month, the male-to-female HIV-transmission risk per contact was found to be 1/769 by direct measurement, a value that falls between the above limits of 1/178 and 1/1548 predicted by the modelling. Thus, a second major prediction of this paper has been directly confirmed, and induced immunity to HIV is limited and not absolutely protective.Circumstantial evidence suggests that the induced immunity to HIV predicted by the model could be generated and/or initiated by nonspecific innate immune responses, specific immunological responses, including IgA-mediated mucosal immunity and cytotoxic T lymphocytes (CTL) immunity, or some combination of the above. It is suggested here, that a decrease in the ability of HIV virions to penetrate the protective mucus layer of the reproductive tract may be a prerequisite, cofactor, or the principle cause of the induced immunity or resistance demonstrated to exist in this paper. The value of the probability that induced immunity to HIV will develop after a contact is shown to be a sensitive function of the woman's human leucocyte antigen (HLA) supertype profile.     

Study on a HIV/AIDS model with application to Yunnan province,China

This paper presents an epidemic model aiming at the prevalence of HIV/AIDS in Yunnan, China. The total population in the model is restricted within high risk population. By the epidemic characteristics of HIV/AIDS in Yunnan province, the population is divided into two groups: injecting drug users (IDUs) and people engaged in commercial sex (PECS) which includes female sex workers (FSWs), and clients of female sex workers (C). For a better understanding of HIV/AIDS transmission dynamics, we do some necessary mathematical analysis. The conditions and thresholds for the existence of four equilibria are established. We compute the reproduction number for each group independently, and show that when both the reproduction numbers are less than unity, the disease-free equilibrium is globally stable. The local stabilities for other equilibria including two boundary equilibria and one positive equilibrium are figured out. When we omit the infectivity of AIDS patients, global stability of these equilibria are obtained. For the simulation, parameters are chosen to fit as much as possible prevalence data publicly available for Yunnan. Increasing strength of the control measure on high risk population is necessary to reduce the HIV/AIDS in Yunnan.     

Exploring express delivery networks in China based on complex network theory

Based on the complex network theory, we explore an express delivery system in China, which consists of two delivery networks, namely, the air delivery network (ADN) and the ground delivery network (GDN). Systematic structural analysis indicates that both delivery networks exhibit small‐world phenomenon, disassortative mixing behavior, and rich‐club phenomenon. However, there are significant differences between ADN and GDN in terms of degree distribution property and community structure. On the basis of the Barabási‐Albert model, we have proposed a network model incorporating the structural features of the two delivery networks to reveal their evolutionary mechanisms. Lastly, the parcel strength and the distance strength are analyzed, which, respectively, reflect the number of parcels and the long‐haul delivery distance handled by a node city. The strengths are highly heterogeneous in both delivery networks and have intense correlations with topological structures. These works are beneficial for express enterprises to construct or extend their express delivery networks, and provide some useful insights on improving parcel delivery service. © 2014 Wiley Periodicals, Inc. Complexity 21: 166–179, 2015     

A probabilistic model to describe the spread of the Human Immunodeficiency Virus by intravenous drug use

In contrast to the majority of mathematical investigations into the dynamics of the spread of the human immunodeficiency virus (HIV), which have been concerned with sexual transmission, this investigation deals with its spread by intravenus drug use (IVDU). An ‘addict based’ approach is presented in which the proportion of the susceptible population to be infected is determined by Monte Carlo means. This is in contrast to a 1989 ‘shooting gallery’ approach by Kaplan.     

Efficient structure of noisy communication networks

In the canonical network model, the connections model, only three specific network structures are generically efficient: complete, empty, and star networks. This renders many plausible network structures inefficient. We show that requiring robustness with respect to stochastic information transmission failures rehabilitates incomplete, redundant network structures. Specifically, we show that star and complete networks are not generally robust to transmission failures, that circular and quasi-circular networks are efficient at intermediate costs in four-player networks, and that if either of them is efficient, then at least one of them is pairwise stable even without reallocation. Thus, incomplete, redundant networks are efficient and stable at intermediate costs.     

Mathematical Analysis of an HIV/AIDS Model: Impact of Educational Programs and Abstinence in Sub-Saharan Africa

We formulate a deterministic HIV/AIDS model to theoretically investigate how counselling and testing coupled with the resulting decrease in sexual activity could affect the HIV epidemic in resource-limited communities. The threshold quantities are determined and stabilities analyzed. Theoretical analysis and numerical simulations support the idea that increase in the number of sexually inactive HIV positive individuals who voluntarily abstain from sex has a positive impact on HIV/AIDS control. Results from this theoretical study suggest that effective counselling and testing have a great potential to partially control the epidemic (especially when HIV positive individuals either willingly withdraw from risky sexual activities or disclose their status beforehand) even in the absence of antiretroviral therapy (ART). Therefore, more needs to be done in resource-limited settings, such as sub-Saharan Africa, as far as the HIV/AIDS epidemic is concerned and a formalized information, education, and communication strategy should be given prominence in educational campaigns.