Endemic threshold results in an age-duration-structured population model for HIV infection

In this paper we consider an age-duration-structured population model for HIV infection in a homosexual community. First we investigate the invasion problem to establish the basic reproduction ratio R(0) for the HIV/AIDS epidemic by which we can state the threshold criteria: The disease can invade into the completely susceptible population if R(0)>1, whereas it cannot if R(0)<1. Subsequently, we examine existence and uniqueness of endemic steady states. We will show sufficient conditions for a backward or a forward bifurcation to occur when the basic reproduction ratio crosses unity. That is, in contrast with classical epidemic models, for our HIV model there could exist multiple endemic steady states even if R(0) is less than one. Finally, we show sufficient conditions for the local stability of the endemic steady states.     

Global dynamics of a staged-progression model with amelioration for infectious diseases

We analyze the global dynamics of a mathematical model for infectious diseases that progress through distinct stages within infected hosts with possibility of amelioration. An example of such diseases is HIV/AIDS that progresses through several stages with varying degrees of infectivity; amelioration can result from a host's immune action or more commonly from antiretroviral therapies, such as highly active antiretroviral therapy. For a general n-stage model with constant recruitment and bilinear incidence that incorporates amelioration, we prove that the global dynamics are completely determined by the basic reproduction number R(0). If R(0)≤1, then the disease-free equilibrium P(0) is globally asymptotically stable, and the disease always dies out. If R(0)>1, P(0) is unstable, a unique endemic equilibrium P* is globally asymptotically stable, and the disease persists at the endemic equilibrium. Impacts of amelioration on the basic reproduction number are also investigated.     

Stochastic and deterministic models for SIS epidemics among a population partitioned into households

Models for the spread of an SIS epidemic among a population consisting of m households, each containing n individuals, are considered and their behaviour is analysed under the practically relevant situation when m is large and n small. A threshold parameter R* is determined. For the stochastic model it is shown that the epidemic has a non-zero probability of taking off if and only if R* > 1, and the extension to unequal household sizes is also considered. For the deterministic model, with households of size 2, it is shown that if R* < or = 1 then the epidemic dies out, whilst if R* > 1 the epidemic settles down to an endemic equilibrium. The usual basic reproductive ratio R0 does not provide a good indicator for the behaviour of these household epidemic models unless the household size n is large.     

Three stage AIDS incubation period: a worst case scenario using addict-needle interaction assumptions

In this paper we develop and analyse a model for the spread of HIV/AIDS amongst a population of injecting drug users. We start off with a brief literature survey and review; this is followed by the derivation of a model which allows addicts to progress through three distinct stages of variable infectivity prior to the onset of full blown AIDS and where the class of infectious needles is split into three according to the different levels of infectivity in addicts. Given the structure of this model we are required to make assumptions regarding the interaction of addicts and needles of different infectivity levels. We deliberately choose these assumptions so that our model serves as an upper bound for the prevalence of HIV under the assumption of a three stage AIDS incubation period. We then perform an equilibrium and stability analysis on this model. We find that there is a critical threshold parameter R(0) which determines the behaviour of the model. If R(0)< or =1, then irrespective of the initial conditions of the system HIV will die out in all addicts and all needles. If R(0)>1, then there is a unique endemic equilibrium which is locally stable if, as is realistic, the time scale on which addicts inject is much shorter than that of the other epidemiological and demographic processes. Simulations indicate that if R(0)>1, then provided that disease is initially present in at least one addict or needle it will tend to the endemic equilibrium. In addition we derive conditions which guarantee this. We also find that under calibration the long term prevalence of disease in our variable infectivity model is always greater than in an equivalent constant infectivity model. These results are confirmed and explored further by simulation. We conclude with a short discussion.     

Theory versus data: how to calculate R0?

To predict the potential severity of outbreaks of infectious diseases such as SARS, HIV, TB and smallpox, a summary parameter, the basic reproduction number R(0), is generally calculated from a population-level model. R(0) specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. R(0) is used to assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventions necessary for control. Conventionally, it is assumed that if R(0)>1 the outbreak generates an epidemic, and if R(0)<1 the outbreak becomes extinct. Here, we use computational and analytical methods to calculate the average number of secondary infections and to show that it does not necessarily represent an epidemic threshold parameter (as it has been generally assumed). Previously we have constructed a new type of individual-level model (ILM) and linked it with a population-level model. Our ILM generates the same temporal incidence and prevalence patterns as the population-level model; we use our ILM to directly calculate the average number of secondary infections (i.e., R(0)). Surprisingly, we find that this value of R(0) calculated from the ILM is very different from the epidemic threshold calculated from the population-level model. This occurs because many different individual-level processes can generate the same incidence and prevalence patterns. We show that obtaining R(0) from empirical contact tracing data collected by epidemiologists and using this R(0) as a threshold parameter for a population-level model could produce extremely misleading estimates of the infectiousness of the pathogen, the severity of an outbreak, and the strength of the medical and/or behavioral interventions necessary for control.     

中国新疆维族人群HLA-B等位基因与HIV-1感染易感性或抗性

通过对中国维吾尔族人群HLA-B等位基因的分布频率的研究,探讨HLA-B等位基因与HIV感染的易感 或抵抗性的相关性。本研究用PCR-SSP的方法对新疆维吾尔族110例无相关的健康对照者(HIV阴性)和128例 HIV阳性感染者进行HLA-B等位基因分型。用POPGEN软件对健康对照者人群进行Hardy-Weinberg平衡检 测,用卡方检验分析HLA-B等位基因在健康对照者和HIV阳性感染者频率分布的差异。在HIV-1阳性感染者 中,B*4901等位基因频率显著性增加(B*4901:P=0．02．OR=3．06,95%CI=1．16～8．10)。而在健埭对照者 中,B*40等位基因顿率增加具有统计意义(B*40:P=0．02．OR=0．39．95％CI=0．07～0．92)。由此可见,B* 4901等位基因可能与HIV-1感染的易感性有关,而B*40等位基因可能与与HIV-1感染的抵抗性有关。     

Analysis of the CCR5 gene coding region diversity in five South American populations reveals two new non-synonymous alleles in Amerindians and high CCR5*D32 frequency in Euro-Brazilians

The CC chemokine receptor 5 (CCR5) molecule is an important co-receptor for HIV. The effect of the CCR5*D32 allele in susceptibility to HIV infection and AIDS disease is well known. Other alleles than CCR5*D32 have not been analysed before, neither in Amerindians nor in the majority of the populations all over the world. We investigated the distribution of the CCR5 coding region alleles in South Brazil and noticed a high CCR5*D32 frequency in the Euro-Brazilian population of the Paraná State (9.3%), which is the highest thus far reported for Latin America. The D32 frequency is even higher among the Euro-Brazilian Mennonites (14.2%). This allele is uncommon in Afro-Brazilians (2.0%), rare in the Guarani Amerindians (0.4%) and absent in the Kaingang Amerindians and the Oriental-Brazilians. R223Q is common in the Oriental-Brazilians (7.7%) and R60S in the Afro-Brazilians (5.0%). A29S and L55Q present an impaired response to β-chemokines and occurred in Afro- and Euro-Brazilians with cumulative frequencies of 4.4% and 2.7%, respectively. Two new non-synonymous alleles were found in Amerindians: C323F (g.3729G > T) in Guarani (1.4%) and Y68C (g.2964A > G) in Kaingang (10.3%). The functional characteristics of these alleles should be defined and considered in epidemiological investigations about HIV-1 infection and AIDS incidence in Amerindian populations.     

中国新疆维族人群HLA-B等位基因与HIV-1感染易感性或抗性

通过对中国维吾尔族人群HLA-B等位基因的分布频率的研究,探讨HLA-B等位基因与HIV感染的易感/或抵抗性的相关性.本研究用PCR-SSP的方法对新疆维吾尔族110例无相关的健康对照者(HIV阴性)和128例HIV阳性感染者进行HLA-B等位基因分型.用POPGEN软件对健康对照者人群进行Hardy-Weinberg平衡检测,用卡方检验分析HLA-B等位基因在健康对照者和HIV阳性感染者频率分布的差异.在HIV-1阳性感染者中,B*4901等位基因频率显著性增加(B*4901P=0.02,OR=3.06,95%CI=1.16～8.10).而在健康对照者中,B*40等位基因频率增加具有统计意义(B*40P=0.02,OR=0.39,95%CI=0.07～0.92).由此可见,B*4901等位基因可能与HIV-1感染的易感性有关,而B*40等位基因可能与与HIV-1感染的抵抗性有关.     

一类带有肝炎B病毒感染的数学模型的全局稳定性分析（英文）

本文主要分析了一类具有肝炎B病毒感染且带有治愈率的典型的数学模型（HBV）.通过稳定性分析,得到了该模型的无病平衡点与地方病平衡点全局稳定的充分条件,并且证明了当基本再生数R0〈1, HBV感染消失;当R0〉1,HBV感染持续.     

A mathematical model for Chagas disease with infection-age-dependent infectivity

In this paper we develop a mathematical model for Chagas disease with infection-age-dependent infectivity. The effects of vector and blood transfusion transmission are considered, and the infected population is structured by the infection age (the time elapsed from infection). The authors identify the basic reproduction ratio R0 and show that the disease can invade into the susceptible population and unique endemic steady state exists if R0 > 1, whereas the disease dies out if R0 is small enough. We show that depending on parameters, backward bifurcation of endemic steady state can occur, so even if R0 < 1, there could exist endemic steady states. We also discuss local and global stability of steady states.     

Human leukocyte antigen B58 supertype and human immunodeficiency virus type 1 infection in native Africans

Human leukocyte antigen (HLA) class I alleles can be grouped into supertypes according to their shared peptide binding properties. We examined alleles of the HLA-B58 supertype (B58s) in treatment-na?ve human immunodeficiency virus type 1 (HIV-1)-seropositive Africans (423 Zambians and 202 Rwandans). HLA-B and HLA-C alleles were resolved to four digits by a combination of molecular methods, and their respective associations with outcomes of HIV-1 infection were analyzed by statistical procedures appropriate for continuous or categorical data. The effects of the individual alleles on natural HIV-1 infection were heterogeneous. In HIV-1 subtype C-infected Zambians, the mean viral load (VL) was lower among B*5703 (P = 0.01) or B*5703-Cw*18 (P < 0.001) haplotype carriers and higher among B*5802 (P = 0.02) or B*5802-Cw*0602 (P = 0.03) carriers. The B*5801-Cw*03 haplotype showed an association with low VL (P = 0.05), whereas B*5801 as a whole did not. Rwandans with HIV-1 subtype A infection showed associations of B*5703 and B*5802 with slow (P = 0.06) and rapid (P = 0.003) disease progression, respectively. In neither population were B*1516-B*1517 alleles associated with more favorable responses. Overall, B58s alleles, individually or as part of an HLA-B-HLA-C haplotype, appeared to have a distinctive impact on HIV-1 infection among native Africans. As presently defined, B58s alleles cannot be considered uniformly protective against HIV/AIDS in every population.     

Molecular Basis for Genetic Resistance of Anopheles gambiae to Plasmodium: Structural Analysis of TEP1 Susceptible and Resistant Alleles

Thioester-containing protein 1 (TEP1) is a central component in the innate immune response of Anopheles gambiae to Plasmodium infection. Two classes of TEP1 alleles, TEP1*S and TEP1*R, are found in both laboratory strains and wild isolates, related by a greater or lesser susceptibility, respectively to both P. berghei and P. falciparum infection. We report the crystal structure of the full-length TEP1*S1 allele which, while similar to the previously determined structure of full-length TEP1*R1, displays flexibility in the N-terminal fragment comprising domains MG1-MG6. Amino acid differences between TEP1*R1 and TEP1*S1 are localized to the TED-MG8 domain interface that protects the thioester bond from hydrolysis and structural changes are apparent at this interface. As a consequence cleaved TEP1*S1 (TEP1*S1_cut) is significantly more susceptible to hydrolysis of its intramolecular thioester bond than TEP1*R1_cut. TEP1*S1_cut is stabilized in solution by the heterodimeric LRIM1/APL1C complex, which preserves the thioester bond within TEP1*S1_cut. These results suggest a mechanism by which selective pressure on the TEP1 gene results in functional variation that may influence the vector competence of A. gambiae towards Plasmodium infection.     

Mathematical Analysis of the Transmission Dynamics of HIV Syphilis Co-infection in the Presence of Treatment for Syphilis

The re-emergence of syphilis has become a global public health issue, and more persons are getting infected, especially in developing countries. This has also led to an increase in the incidence of human immunodeficiency virus (HIV) infections as some studies have shown in the recent decade. This paper investigates the synergistic interaction between HIV and syphilis using a mathematical model that assesses the impact of syphilis treatment on the dynamics of syphilis and HIV co-infection in a human population where HIV treatment is not readily available or accessible to HIV-infected individuals. In the absence of HIV, the syphilis-only model undergoes the phenomenon of backward bifurcation when the associated reproduction number (\({\mathcal {R}}_{T}\)) is less than unity, due to susceptibility to syphilis reinfection after recovery from a previous infection. The complete syphilis–HIV co-infection model also undergoes the phenomenon of backward bifurcation when the associated effective reproduction number (\({\mathcal {R}}_{C}\)) is less than unity for the same reason as the syphilis-only model. When susceptibility to syphilis reinfection after treatment is insignificant, the disease-free equilibrium of the syphilis-only model is shown to be globally asymptotically stable whenever the associated reproduction number (\({\mathcal {R}}_{T}\)) is less than unity. Sensitivity and uncertainty analysis show that the top three parameters that drive the syphilis infection (with respect to the associated response function, \({\mathcal {R}}_{T}\)) are the contact rate (\(\beta _S\)), modification parameter that accounts for the increased infectiousness of syphilis-infected individuals in the secondary stage of the infection (\(\theta _1\)) and treatment rate for syphilis-only infected individuals in the primary stage of the infection (\(r_1\)). The co-infection model was numerically simulated to investigate the impact of various treatment strategies for primary and secondary syphilis, in both singly and dually infected individuals, on the dynamics of the co-infection of syphilis and HIV. It is observed that if concerted effort is exerted in the treatment of primary and secondary syphilis (in both singly and dually infected individuals), especially with high treatment rates for primary syphilis, this will result in a reduction in the incidence of HIV (and its co-infection with syphilis) in the population.     

Stability of a Stochastic Model of an SIR Epidemic with Vaccination

We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue \(\mathcal{R}_\sigma\) of the basic reproduction number \(\mathcal{R}_0\) of the underlying deterministic model, with \(\mathcal{R}_\sigma \le \mathcal{R}_0\). We prove that the disease-free equilibrium is almost sure exponentially stable if \(\mathcal{R}_\sigma <1\).     

Dynamical analysis of a multi-strain model of HIV in the presence of anti-retroviral drugs

One major drawback associated with the use of anti-retroviral drugs in curtailing HIV spread in a population is the emergence and transmission of HIV strains that are resistant to these drugs. This paper presents a deterministic HIV treatment model, which incorporates a wild (drug sensitive) and a drug-resistant strain, for gaining insights into the dynamical features of the two strains, and determining effective ways to control HIV spread under this situation. Rigorous qualitative analysis of the model reveals that it has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold (R t 0) is less than unity and that the disease will persist in the population when this threshold exceeds unity. Further, for the case where R t 0 > 1, it is shown that the model can have two co-existing endemic equilibria, and competitive exclusion phenomenon occurs whenever the associated reproduction number of the resistant strain (R t r) is greater than that of the wild strain (R t w). Unlike in the treatment model, it is shown that the model without treatment can have a family of infinitely many endemic equilibria when its associated epidemiological threshold (R(0)) exceeds unity. For the case when [Formula in text], it is shown that the widespread use of treatment against the wild strain can lead to its elimination from the community if the associated reduction in infectiousness of infected individuals (treated for the wild strain) does not exceed a certain threshold value (in this case, the use of treatment is expected to make R t w < R t r.     

The effect of increased background resistance on the resistive load threshold for eliciting the respiratory-related evoked potential.

The detection threshold (DeltaR(50)) of resistive (R) loads is a function of the total background resistance (R(0)). Increased R(0) increases the DeltaR(50), but the ratio DeltaR(50)/R(0) remains constant. The respiratory-related evoked potential (RREP) is elicited only by R loads greater than the cognitive detection threshold, DeltaR(50). We hypothesized that the RREP Nf, P1, and N1 peaks will be elicited only when the added load DeltaR/R(0) is greater than the normal detection threshold, DeltaR(50)/R(0) = 0.30. We also hypothesized that when the R(0) is increased by adding extrinsic R, the RREP will not be elicited if the DeltaR/R(0) is less than the 0.30 ratio. RREPs were recorded with healthy volunteers (n = 20) respiring through a non-rebreathing valve. Three inspiratory R loads that spanned the DeltaR(50)/R(0) = 0.30 detection threshold were presented in two conditions: 1) no added R(0) (R1 < 0.30, R2 > 0.30, R3 > 0.30); and 2) increased R(0) = 13.3 cmH(2)O.l(-1).s (R1 < 0.30, R2 < 0.30, R3 > 0.30). For the control R(0), P1, Nf, and N1 peaks of the RREP were elicited by both R2 and R3, and not present with R1. The increased R(0) decreased R2/R(0) > 1.5 to R2/R(0) < 0.15. With increased R(0), the R1 and R2 loads did not elicit the RREP, but the Nf, P1, and N1 peaks were present for R3. These results demonstrate that the RREP is present if the DeltaR is above the cognitive detection threshold, and the RREP is absent if the load is below the detection threshold. When the R(0) is increased to make the DeltaR/R(0) less than the detection threshold, the DeltaR no longer elicits the RREP.     

Location of the permeation pathway in the recombinant type 1 inositol 1,4,5-trisphosphate receptor.

The inositol 1,4,5-trisphosphate receptor (InsP(3)R) forms ligand-regulated intracellular Ca(2+) release channels in the endoplasmic reticulum of all mammalian cells. The InsP(3)R has been suggested to have six transmembrane regions (TMRs) near its carboxyl terminus. A TMR-deletion mutation strategy was applied to define the location of the InsP(3)R pore. Mutant InsP(3)Rs were expressed in COS-1 cells and single channel function was defined in planar lipid bilayers. Mutants having the fifth and sixth TMR (and the interceding lumenal loop), but missing all other TMRs, formed channels with permeation properties similar to wild-type channels (gCs = 284; gCa = 60 pS; P(Ca)/P(Cs) = 6.3). These mutant channels bound InsP(3), but ligand occupancy did not regulate the constitutively open pore (P(o) > 0.80). We propose that a region of 191 amino acids (including the fifth and sixth TMR, residues 2398-2589) near the COOH terminus of the protein forms the InsP(3)R pore. Further, we have produced a constitutively open InsP(3)R pore mutant that is ideal for future site-directed mutagenesis studies of the structure-function relationships that define Ca(2+) permeation through the InsP(3)R channel.     

Multiple steps of phosphorylation of activated rhodopsin can account for the reproducibility of vertebrate rod single-photon responses

Single-photon responses (SPRs) in vertebrate rods are considerably less variable than expected if isomerized rhodopsin (R*) inactivated in a single, memoryless step, and no other variability-reducing mechanisms were available. We present a new stochastic model, the core of which is the successive ratcheting down of R* activity, and a concomitant increase in the probability of quenching of R* by arrestin (Arr), with each phosphorylation of R* (Gibson, S.K., J.H. Parkes, and P.A. Liebman. 2000. Biochemistry. 39:5738-5749.). We evaluated the model by means of Monte-Carlo simulations of dim-flash responses, and compared the response statistics derived from them with those obtained from empirical dim-flash data (Whitlock, G.G., and T.D. Lamb. 1999. Neuron. 23:337-351.). The model accounts for four quantitative measures of SPR reproducibility. It also reproduces qualitative features of rod responses obtained with altered nucleotide levels, and thus contradicts the conclusion that such responses imply that phosphorylation cannot dominate R* inactivation (Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836-1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733-747.). Moreover, the model is able to reproduce the salient qualitative features of SPRs obtained from mouse rods that had been genetically modified with specific pathways of R* inactivation or Ca2+ feedback disabled. We present a theoretical analysis showing that the variability of the area under the SPR estimates the variability of integrated R* activity, and can provide a valid gauge of the number of R* inactivation steps. We show that there is a heretofore unappreciated tradeoff between variability of SPR amplitude and SPR duration that depends critically on the kinetics of inactivation of R* relative to the net kinetics of the downstream reactions in the cascade. Because of this dependence, neither the variability of SPR amplitude nor duration provides a reliable estimate of the underlying variability of integrated R* activity, and cannot be used to estimate the minimum number of R* inactivation steps. We conclude that multiple phosphorylation-dependent decrements in R* activity (with Arr-quench) can confer the observed reproducibility of rod SPRs; there is no compelling need to invoke a long series of non-phosphorylation dependent state changes in R* (as in Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836-1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733-747.). Our analyses, plus data and modeling of others (Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836-1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733-747.), also argue strongly against either feedback (including Ca2+-feedback) or depletion of any molecular species downstream to R* as the dominant cause of SPR reproducibility.     

Transgenically expressed viral RNA silencing suppressors interfere with microRNA methylation in Arabidopsis

HEN1-dependent methylation of the 3'-terminal nucleotide is a crucial step in plant microRNA (miRNA) biogenesis. Here we report that several viral RNA silencing suppressors (P1/HC-Pro, p21 and p19) inhibit miRNA methylation. These suppressors have distinct effects on different miRNAs. We also show that miRNA* is methylated in vivo in a suppressor-sensitive manner, suggesting that the viral proteins interfere with miRNA/miRNA* duplexes. p19 and p21 bind both methylated and unmethylated miRNA/miRNA* duplexes in vivo. These findings suggest miRNA/miRNA* as the in vivo substrates for the HEN1 miRNA methyltransferase and raise intriguing possibilities regarding the cellular location of miRNA methylation.     

HLA-A*7401-mediated control of HIV viremia is independent of its linkage disequilibrium with HLA-B*5703

The potential contribution of HLA-A alleles to viremic control in chronic HIV type 1 (HIV-1) infection has been relatively understudied compared with HLA-B. In these studies, we show that HLA-A*7401 is associated with favorable viremic control in extended southern African cohorts of >2100 C-clade-infected subjects. We present evidence that HLA-A*7401 operates an effect that is independent of HLA-B*5703, with which it is in linkage disequilibrium in some populations, to mediate lowered viremia. We describe a novel statistical approach to detecting additive effects between class I alleles in control of HIV-1 disease, highlighting improved viremic control in subjects with HLA-A*7401 combined with HLA-B*57. In common with HLA-B alleles that are associated with effective control of viremia, HLA-A*7401 presents highly targeted epitopes in several proteins, including Gag, Pol, Rev, and Nef, of which the Gag epitopes appear immunodominant. We identify eight novel putative HLA-A*7401-restricted epitopes, of which three have been defined to the optimal epitope. In common with HLA-B alleles linked with slow progression, viremic control through an HLA-A*7401-restricted response appears to be associated with the selection of escape mutants within Gag epitopes that reduce viral replicative capacity. These studies highlight the potentially important contribution of an HLA-A allele to immune control of HIV infection, which may have been concealed by a stronger effect mediated by an HLA-B allele with which it is in linkage disequilibrium. In addition, these studies identify a factor contributing to different HIV disease outcomes in individuals expressing HLA-B*5703.