Analysis of HIV models with two time delays

A study on the transmission dynamics of COVID-19 considering the impact of asymptomatic infection

The COVID-19 epidemic has been spreading around the world for nearly three years, and asymptomatic infections have exacerbated the spread of the epidemic. To analyse and evaluate the role of asymptomatic infections in the spread of the epidemic, we establish an improved COVID-19 infectious disease dynamics model. We fit the epidemic data in the four time periods corresponding to the selected 614G, Alpha, Delta and Omicron variants and obtain the proportion of asymptomatic persons among the infected persons gradually increased and with the increase of the detection ratio, the cumulative number of cases has dropped significantly, but the decline in the proportion of asymptomatic infections is not obvious. Therefore, in view of the hidden transmission of asymptomatic infections, the cooperation between various epidemic prevention and control policies is required to effectively curb the spread of the epidemic.

Analysis of HIV latent infection model with multiple infection stages and different drug classes

Latently infected CD4+ T cells represent one of the major obstacles to HIV eradication even after receiving prolonged highly active anti-retroviral therapy (HAART). Long-term use of HAART causes the emergence of drug-resistant virus which is then involved in HIV transmission. In this paper, we develop mathematical HIV models with staged disease progression by incorporating entry inhibitor and latently infected cells. We find that entry inhibitor has the same effect as protease inhibitor on the model dynamics and therefore would benefit HIV patients who developed resistance to many of current anti-HIV medications. Numerical simulations illustrate the theoretical results and show that the virus and latently infected cells reach an infected steady state in the absence of treatment and are eliminated under treatment whereas the model including homeostatic proliferation of latently infected cells maintains the virus at low level during suppressive treatment. Therefore, complete cure of HIV needs complete eradication of latent reservoirs.

Uniform Persistence and Global Attractivity in a Delayed Virus Dynamic Model with Apoptosis and Both Virus-to-Cell and Cell-to-Cell Infections

In this paper, we study the global dynamics of a delayed virus dynamics model with apoptosis and both virus-to-cell and cell-to-cell infections. When the basic reproduction number R0>1, we obtain the uniform persistence of the model, and give some explicit expressions of the ultimate upper and lower bounds of any positive solution of the model. In addition, by constructing the appropriate Lyapunov functionals, we obtain some sufficient conditions for the global attractivity of the disease-free equilibrium and the chronic infection equilibrium of the model. Our results extend existing related works.

Intra- and Inter-cellular Modeling of Dynamic Interaction between Zika Virus and Its Naturally Occurring Defective Viral Genomes

Here, we examine in silico the infection dynamics and interactions of two Zika virus (ZIKV) genomes: one is the full-length ZIKV genome (wild type [WT]), and the other is one of the naturally occurring defective viral genomes (DVGs), which can replicate in the presence of the WT genome, appears under high-MOI (multiplicity of infection) passaging conditions, and carries a deletion encompassing part of the structural and NS1 protein-coding region. Ordinary differential equations (ODEs) were used to simulate the infection of cells by virus particles and the intracellular replication of the WT and DVG genomes that produce these particles. For each virus passage in Vero and C6/36 cell cultures, the rates of the simulated processes were fitted to two types of observations: virus titer data and the assembled haplotypes of the replicate passage samples. We studied the consistency of the model with the experimental data across all passages of infection in each cell type separately as well as the sensitivity of the model's parameters. We also determined which simulated processes of virus evolution are the most important for the adaptation of the WT and DVG interplay in these two disparate cell culture environments. Our results demonstrate that in the majority of passages, the rates of DVG production are higher inC6/36 cells than in Vero cells, which might result in tolerance and therefore drive the persistence of the mosquito vector in the context of ZIKV infection. Additionally, the model simulations showed a slower accumulation of infected cells under higher activation of the DVG-associated processes, which indicates a potential role of DVGs in virus attenuation. IMPORTANCE One of the ideas for lessening Zika pathogenicity is the addition of its natural or engineered defective virus genomes (DVGs) (have no pathogenicity) to the infection pool: a DVG is redirecting the wild-type (WT)-associated virus development resources toward its own maturation. The mathematical model presented here, attuned to the data from interplays between WT Zika viruses and their natural DVGs in mammalian and mosquito cells, provides evidence that the loss of uninfected cells is attenuated by the DVG development processes. This model enabled us to estimate the rates of virus development processes in the WT/DVG interplay, determine the key processes, and show that the key processes are faster in mosquito cells than in mammalian ones. In general, the presented model and its detailed study suggest in what important virus development processes the therapeutically efficient DVG might compete with the WT; this may help in assembling engineered DVGs for ZIKV and other flaviviruses.

A mathematical model of HIV dynamics treated with a population of gene-edited haematopoietic progenitor cells exhibiting threshold phenomenon

The use of gene-editing technology has the potential to excise the CCR5 gene from haematopoietic progenitor cells, rendering their differentiated CD4-positive (CD4+) T cell descendants HIV resistant. In this manuscript, we describe the development of a mathematical model to mimic the therapeutic potential of gene editing of haematopoietic progenitor cells to produce a class of HIV-resistant CD4+ T cells. We define the requirements for the permanent suppression of viral infection using gene editing as a novel therapeutic approach. We develop non-linear ordinary differential equation models to replicate HIV production in an infected host, incorporating the most appropriate aspects found in the many existing clinical models of HIV infection, and extend this model to include compartments representing HIV-resistant immune cells. Through an analysis of model equilibria and stability and computation of $R_0$ for both treated and untreated infections, we show that the proposed therapy has the potential to suppress HIV infection indefinitely and return CD4+ T cell counts to normal levels. A computational study for this treatment shows the potential for a successful 'functional cure' of HIV. A sensitivity analysis illustrates the consistency of numerical results with theoretical results and highlights the parameters requiring better biological justification. Simulations of varying level production of HIV-resistant CD4+ T cells and varying immune enhancements as the result of these indicate a clear threshold response of the model and a range of treatment parameters resulting in a return to normal CD4+ T cell counts.

Modeling Intracellular Delay in Within-Host HIV Dynamics Under Conditioning of Drugs of Abuse

Drugs of abuse, such as opiates, have been widely associated with the enhancement of HIV replication, the acceleration of disease progression, and severe neuropathogenesis. Specifically, the presence of drugs of abuse (morphine) switches target cells (CD4[Formula: see text] T cells) from lower-to-higher susceptibility to HIV infection. The effect of such switching behaviors on viral dynamics may be altered due to the intracellular delay (the replication time between viral entry into a target cell and the production of new viruses by the infected cell). In this study, we develop, for the first time, a viral dynamics model that includes an intracellular delay under the conditioning of drugs of abuse. We parameterize the model using experimental data from simian immunodeficiency virus infection of morphine-addicted macaques. Results from thorough mathematical analyses and numerical simulations of our model show that the intracellular delay can play a significant role in HIV dynamics under the conditioning of drugs of abuse, particularly during the acute phase of infection. Our model and the related results provide new insights into the HIV dynamics and may help develop strategies to control HIV infections in drug abusers.

Viral dynamics of a latent HIV infection model with Beddington-DeAngelis incidence function, B-cell immune response and multiple delays

In this paper, an HIV infection model with latent infection, Beddington-DeAngelis infection function, B-cell immune response and four time delays is formulated. The well-posedness of the model solution is rigorously derived, and the basic reproduction number $\mathcal{R}_0$ and the B-cell immune response reproduction number $\mathcal{R}_1$ are also obtained. By analyzing the modulus of the characteristic equation and constructing suitable Lyapunov functions, we establish the global asymptotic stability of the uninfected and the B-cell-inactivated equilibria for the four time delays, respectively. Hopf bifurcation occurs at the B-cell-activated equilibrium when the model includes the immune delay, and the B-cell-activated equilibrium is globally asymptotically stable if the model does not include it. Numerical simulations indicate that the increase of the latency delay, the cell infection delay and the virus maturation delay can cause the B-cell-activated equilibrium stabilize, while the increase of the immune delay can cause it destabilize.

Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation

A mathematical model composed of two non-linear differential equations that describe the population dynamics of CD4 T-cells in the human immune system, as well as viral HIV viral load, is proposed. The invariance region is determined, classical equilibrium stability analysis is performed by using the basic reproduction number, and numerical simulations are carried out to illustrate stability results. Thereafter, the model is modified with a delay term, describing the time required for CD4 T-cell immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations. For the new model, equilibriums are determined, their local stability is examined, and results are studied by way of numerical simulation.

Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions

In this paper, we construct an Human immunodeficiency virus (HIV) dynamics model with impairment of B-cell functions and the general incidence rate. We incorporate three types of infected cells, (i) latently-infected cells, which contain the virus, but do not generate HIV particles, (ii) short-lived productively-infected cells, which live for a short time and generate large numbers of HIV particles, and (iii) long-lived productively-infected cells, which live for a long time and generate small numbers of HIV particles. The model considers five distributed time delays to characterize the time between the HIV contact of an uninfected CD4 + T-cell and the creation of mature HIV. The nonnegativity and boundedness of the solutions are proven. The model admits two equilibria, infection-free equilibrium E P 0 and endemic equilibrium E P 1 . We derive the basic reproduction number R 0 , which determines the existence and stability of the two equilibria. The global stability of each equilibrium is proven by utilizing the Lyapunov function and LaSalle’s invariance principle. We prove that if R 0 < 1 , then E P 0 is globally asymptotically stable, and if R 0 > 1 , then E P 1 is globally asymptotically stable. These theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions, time delays, and antiviral treatment on the HIV dynamics are studied. We show that if the functions of B-cells are impaired, then the concentration of HIV is increased in the plasma. Moreover, we observe that the time delay has a similar effect to drug efficacy. This gives some impression for developing a new class of treatments to increase the delay period and then suppress the HIV replication.

Analysis of latent CHIKV dynamics models with general incidence rate and time delays

In this paper, we study the stability analysis of latent Chikungunya virus (CHIKV) dynamics models. The incidence rate between the CHIKV and the uninfected monocytes is modelled by a general nonlinear function which satisfies a set of conditions. The model is incorporated by intracellular discrete or distributed time delays. Using the method of Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

Stability of latent pathogen infection model with adaptive immunity and delays

In this paper we propose and analyze a pathogen dynamics model with antibody and Cytotoxic T Lymphocyte (CTL) immune responses. We incorporate latently infected cells and three distributed time delays into the model. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters which fully determine the existence and stability of the five steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.

Mathematical analysis of an HIV latent infection model including both virus-to-cell infection and cell-to-cell transmission

HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states. Numerical simulations have been performed to illustrate the theoretical results and evaluate the effects of time delays and fractions of infection leading to latency on the virus dynamics. The estimates of the relative contributions to the HIV latent reservoir and the virus population from the two modes of transmission have also been provided.