HIV-1 can disseminate between susceptible cells by two mechanisms: cell-free infection following fluid-phase diffusion of virions and by highly-efficient direct cell-to-cell transmission at immune cell contacts. The contribution of this hybrid spreading mechanism, which is also a characteristic of some important computer worm outbreaks, to HIV-1 progression in vivo remains unknown. Here we present a new mathematical model that explicitly incorporates the ability of HIV-1 to use hybrid spreading mechanisms and evaluate the consequences for HIV-1 pathogenenesis. The model captures the major phases of the HIV-1 infection course of a cohort of treatment naive patients and also accurately predicts the results of the Short Pulse Anti-Retroviral Therapy at Seroconversion (SPARTAC) trial. Using this model we find that hybrid spreading is critical to seed and establish infection, and that cell-to-cell spread and increased CD4+ T cell activation are important for HIV-1 progression. Notably, the model predicts that cell-to-cell spread becomes increasingly effective as infection progresses and thus may present a considerable treatment barrier. Deriving predictions of various treatments' influence on HIV-1 progression highlights the importance of earlier intervention and suggests that treatments effectively targeting cell-to-cell HIV-1 spread can delay progression to AIDS. This study suggests that hybrid spreading is a fundamental feature of HIV infection, and provides the mathematical framework incorporating this feature with which to evaluate future therapeutic strategies.
Robustness of a Cellular Automata Model for the HIV Infection
进行了一项调查，以研究从描述HIV感染在淋巴组织内传播的元胞自动机模型获得的结果的稳健性[R. M. Zorzenon dos Santos和S. Coutinho，Phys. Rev. Lett. 87，168102（2001）]。分析集中在具有不同对称性和维数的晶格中定义的模型的动态行为。结果表明，三相动力学的平面模型的晶格对称性的变化发生轻微的变化，而观察到的差异，关于维度的变化，定性行为被保留。进一步的调查进行了初级感染和敏感性的潜伏期变化的模型的随机参数在很宽的范围内的值。当随机参数在几个数量级上变化时，表征原发感染和潜伏期的变量表现出幂律行为。当晶格对称性改变时，幂律指数大致相同，但当维数从2变为3时，幂律指数有显著变化。三维模型的动力学也被证明是不敏感的确定性参数的变化与细胞抵抗感染，和必要的时间滞后，安装特定的免疫反应，艾滋病毒变种。在这项工作中所证明的模型的鲁棒性加强了其基本假设与在患者中观察到的HIV感染的三阶段动态一致。
We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of uninfected CD4+ T cells by a logistic function and the infected CD4+ T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some pa…
Oxidative stress, a reaction caused by the imbalance between the reactive oxygen species of human organism and its ability to detoxify reactive intermediates and to repair the resulting damage plays an important role in HIV-infections. On one hand, HIV infection is responsible for the chronic oxidative stress of the patients. On the other hand, the oxidative stress contributions to the HIV disease pathogenesis. In this paper, we integrate oxidative stress into an HIV infection model to investigate its effects on the virus dynamics. Through mathematical analysis, we obtain the basic reproductio…
Amsterdam and other UNAIDS Fast-Track cities aim for zero new HIV infections. Utilising molecular and clinical data of the ATHENA observational HIV cohort, our primary aims are to estimate the proportion of undiagnosed HIV infections and the proportion of locally acquired infections in Amsterdam in 2014-2018, both in MSM and heterosexuals and Dutch-born and foreign-born individuals. We located diagnosed HIV infections in Amsterdam using postcode data at time of registration to the cohort, and estimated their date of infection using clinical HIV data. We then inferred the proportion undiagnosed…
We propose a population model for HIV-TB co-infection dynamics by considering treatments for HIV infection, active tuberculosis and co-infection. The HIV only and TB only models are analyzed separately, as well as full model. The basic reproduction numbers for TB ($\mathcal{R}_0^T$) and HIV ($\mathcal{R}_0^H$) and overall reproduction number for the system $\mathcal{R}_0= \max\{\mathcal{R}_0^T, \mathcal{R}_0^H\}$ are computed. The equilibria and their stability are studied. The main model undergoes supercritical transcritical bifurcation at $\mathcal{R}_0^T=1$ and $\mathcal{R}_0^H=1$ whereas t…
Recent clinical studies have shown that HIV disease pathogenesis can depend strongly on many factors at the time of transmission, including the strength of the initial viral load and the local availability of CD4+ T-cells. In this article, a new within-host model of HIV infection that incorporates the homeostatic proliferation of T-cells is formulated and analyzed. Due to the effects of this biological process, the influence of initial conditions on the proliferation of HIV infection is further elucidated. The identifiability of parameters within the model is investigated and a local stability…
We define and examine a model of epidemic propagation for a virus such as Hepatitis C (with HIV co-infection) on a network of networks, namely the network of French urban areas. One network level is that of the individual interactions inside each urban area. The second level is that of the areas themselves, linked by individuals travelling between these areas and potentially helping the epidemic spread from one city to another. We choose to encode the second level of the network as extra, special nodes in the first level. We observe that such an encoding leads to sensible results in terms of t…
We study the global dynamics of a SICA infection model with general incidence rate. The proposed model is calibrated with cumulative cases of infection by HIV-AIDS in Morocco from 1986 to 2015. We first prove that our model is biologically and mathematically well-posed. Stability analysis of different steady states is performed and threshold parameters are identified where the model exhibits clearance of infection or maintenance of a chronic infection. Furthermore, we examine the robustness of the model to some parameter values by examining the sensitivity of the basic reproduction number. Fin…
Random mixing in host populations has been a convenient simplifying assumption in the study of epidemics, but neglects important differences in contact rates within and between population groups. For HIV/AIDS, the assumption of random mixing is inappropriate for epidemics that are concentrated in groups of people at high risk, including female sex workers (FSW) and their male clients (MCF), injection drug users (IDU) and men who have sex with men (MSM). To find out who transmits infection to whom and how that affects the spread and containment of infection remains a major empirical challenge i…
In this paper, we construct a model to describe the transmission of HIV in a homogeneous host population. By considering the specific mechanism of HIV, we derive a model structured in three successive stages: (i) primary infection, (ii) long phase of latency without symptoms and (iii) AIDS. Each HIV stage is stratified by the duration for which individuals have been in the stage, leading to a continuous age-structure model. In the first part of the paper, we provide a global analysis of the model depending upon the basic reproduction number R 0. When R 0 $\le$ 1, then the disease-free equilibr…
We propose a time-parameterized analogy between the thermodynamic behavior of a 3-level energy system and the progression of the HIV infection described by the cell population evolution generated by an appropriated cellular automata model. The development of internal energy and its fluctuations, and of the entropy of the 3-level energy system allows the identification of an effective temperature that uniquely characterizes the three main stages of the dynamic process of HIV infection. Furthermore, this thermodynamical equivalence allows obtaining the instants associated with particular time in…
In this paper, we investigate a novel 3-compartment model of HIV infection of CD4$^+$ T-cells with a mass action term by including two versions: one baseline ODE model and one delay-differential equation (DDE) model with a constant discrete time delay. Similar to various endemic models, the dynamics within the ODE model is fully determined by the basic reproduction term $R_0$. If $R_0<1$, the disease-free (zero) equilibrium will be asymptotically stable and the disease gradually dies out. On the other hand, if $R_0>1$, there exists a positive equilibrium that is globally/orbitally asymptotical…
Semi-Quantitative Analysis and Seroepidemiological Evidence of Past Dengue Virus Infection among HIV-infected patients in Onitsha, Anambra State, Nigeria
Modeling the effects of tetanus vaccination on chronically infected HIV patients
T细胞活化在HIV-1感染的起始和传播中起关键作用，然而免疫系统的瞬时活化是对免疫的正常应答。在这项研究中，我们扩展了一个简单的艾滋病毒感染模型，包括T细胞激活疫苗接种。然后，我们表明，该模型可以重现Stanley等人观察和报告的破伤风免疫后病毒载量上升的许多但不是全部特征，[N. Engl. J. Med.，334：1222- 1230（1996）]。免疫后最大病毒血症的振幅和大致时间在9/12例中匹配;在具有几乎相等振幅的双峰的患者中，较晚的峰匹配。在病毒血症中具有单个早期峰值的患者最适合具有相对高的抗原清除率常数，而在病毒血症中具有相等或几乎相等幅度的早期和晚期峰值的患者最适合具有低得多的清除率。清除率可能取决于预先存在的抗体水平，而预先存在的抗体水平又可能取决于研究中的个体接受既往破伤风疫苗接种的时间。
We will study a mathematical model of the human immunodeficiency virus (HIV) infection in the presence of combination therapy that includes within-host infectious dynamics. The deterministic model requires us to analyze asymptotic stability of two distinct steady states, disease-free and endemic equilibria. Previous results have focused on investigating the global asymptotic stability of the trivial steady state using an implicit finite-difference method which generates a system of difference equations. We, instead, provide analytic solutions and long term attractive behavior for the endemic s…
Pre-exposure prophylaxis (PrEP) consists in the use of an antiretroviral medication to prevent the acquisition of HIV infection by uninfected individuals and has recently demonstrated to be highly efficacious for HIV prevention. We propose a new epidemiological model for HIV/AIDS transmission including PrEP. Existence, uniqueness and global stability of the disease free and endemic equilibriums are proved. The model with no PrEP is calibrated with the cumulative cases of infection by HIV and AIDS reported in Cape Verde from 1987 to 2014, showing that it predicts well such reality. An optimal c…
The search to understand how the HIV virus spreads inside the human body and how the immune response works to control it has motivated studies related to Mathematical Immunology. Actually, researches include the idea of mathematical models representing the dynamics of healthy and infected cell populations and focusing on mechanisms used by HIV to invade target-host cells, viral dissemination (which leads to depletion of the T-cell pool and collapse of the immune system), and impairment of immune response. In this work, we show the importance of specific cells of immune response, as infection v…
We investigate the celebrated mathematical SICA model but using fractional differential equations in order to better describe the dynamics of HIV-AIDS infection. The infection process is modelled by a general functional response and the memory effect is described by the Caputo fractional derivative. Stability and instability of equilibrium points are determined in terms of the basic reproduction number. Furthermore, a fractional optimal control system is formulated and the best strategy for minimizing the spread of the disease into the population is determined through numerical simulations bas…
Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using macroscopic parameters that do not accurately represent person-to-person variability. To address this issue, we present a dynamic network model that provides a straightforward way to incorporate both disease transmission dynamics at the individual scale as well as the full spatiotemporal history of infection at the population scale. We find that disease spreads …
The epidemic spreading has been widely studied when each node may get infected by an infected neighbor with the same rate. However, the infection rate between a pair of nodes is usually heterogeneous and even correlated with their nodal degrees in the contact network. We aim to understand how such correlated heterogeneous infection rates influence the spreading on different network topologies. Motivated by real-world datasets, we propose a correlated heterogeneous Susceptible-Infected-Susceptible model which assumes that the infection rate $β_{ij}(=β_{ji})$ between node $i$ and $j$ is correlat…
The vertebrate adaptive immune system provides a flexible and diverse set of molecules to neutralize pathogens. Yet, viruses such as HIV can cause chronic infections by evolving as quickly as the adaptive immune system, forming an evolutionary arms race. Here we introduce a mathematical framework to study the coevolutionary dynamics of antibodies with antigens within a host. We focus on changes in the binding interactions between the antibody and antigen populations, which result from the underlying stochastic evolution of genotype frequencies driven by mutation, selection, and drift. We ident…
We propose to use the mean time between infections (MTBI) metric as obtained from a recently introduced non-homogeneous Markov stochastic model. Different types of parameter calibration are performed. We estimate the MTBI using data from different time windows and from the whole stage history and compare the results. In order to detect waves and stages in the input data, a preprocessing filtering technique is applied. The results of applying this indicator to the COVID-19 reported data of infections from Argentina, Germany and the United States are shown. We find that the MTBI behaves similarl…
We introduce an epidemic spreading model on a network using concepts from percolation theory. The model is motivated by discussing the standard SIR model, with extensions to describe effects of lockdowns within a population. The underlying ideas and behavior of the lattice model, implemented using the same lockdown scheme as for the SIR scheme, are discussed in detail and illustrated with extensive simulations. A comparison between both models is presented for the case of COVID-19 data from the USA. Both fits to the empirical data are very good, but some differences emerge between the two appr…
Northwestern University（西北大学）；NSF-Simons National Institute for Theory and Mathematics in Biology（NSF-西蒙斯生物理论与数学国家研究所）；Northwestern Institute on Complex Systems, Northwestern University（西北大学复杂系统研究所）；Department of Engineering Sciences and Applied Mathematics, Northwestern University（西北大学工程科学与应用数学系）
The epidemic spreading has been studied for years by applying the mean-field approach in both homogeneous case, where each node may get infected by an infected neighbor with the same rate, and heterogeneous case, where the infection rates between different pairs of nodes are different. Researchers have discussed whether the mean-field approaches could accurately describe the epidemic spreading for the homogeneous cases but not for the heterogeneous cases. In this paper, we explore under what conditions the mean-field approach could perform well when the infection rates are heterogeneous. In pa…
We investigate spreading and recovery of disease in a square lattice, and in particular, emphasize the role of the initial distribution of infected patches in the network, on the progression of an endemic and initiation of a recovery process, if any, due to migration of both the susceptible and infected hosts. The disease starts in the lattice with three possible initial distribution patterns of infected and infection-free sites, infected core patches (ICP), infected peripheral patches (IPP) and randomly distributed infected patches (RDIP). Our results show that infection spreads monotonically…
Broadly neutralizing antibodies are promising candidates for treatment and prevention of HIV-1 infections. Such antibodies can temporarily suppress viral load in infected individuals; however, the virus often rebounds by escape mutants that have evolved resistance. In this paper, we map an in vivo fitness landscape of HIV-1 interacting with broadly neutralizing antibodies, using data from a recent clinical trial. We identify two fitness factors, antibody dosage and viral load, that determine viral reproduction rates reproducibly across different hosts. The model successfully predicts the escap…
