Global stability of secondary DENV infection models with non-specific and strain-specific CTLs

Dengue virus (DENV) is a highly perilous virus that is transmitted to humans through mosquito bites and causes dengue fever. Consequently, extensive efforts are being made to develop effective treatments and vaccines. Mathematical modeling plays a significant role in comprehending the dynamics of DENV within a host in the presence of cytotoxic T lymphocytes (CTL) immune response. This study examines two models for secondary DENV infections that elucidate the dynamics of DENV under the influence of two types of CTL responses, namely non-specific and strain-specific responses. The first model encompasses five compartments, which consist of uninfected monocytes, infected monocytes, free DENV particles, non-specific CTLs, and strain-specific CTLs. In the second model, latently infected cells are introduced into the model. We posit that the CTL responsiveness is determined by a combination of self-regulating CTL response and a predator-prey-like CTL response. The model's solutions are verified to be nonnegativity and bounded and the model possesses two equilibrium states: the uninfected equilibrium EQ 0 and the infected equilibrium EQ ⁎ . Furthermore, we calculate the basic reproduction number R 0 , which determines the existence and stability of the model's equilibria. We examine the global stability by constructing suitable Lyapunov functions. Our analysis reveals that if R 0 ≤ 1 , then EQ 0 is globally asymptotically stable (G.A.S), and if R 0 > 1 , then EQ 0 is unstable while EQ ⁎ is G.A.S. To illustrate our findings analytically, we conduct numerical simulations for each model. Additionally, we perform sensitivity analysis to demonstrate how the parameter values of the proposed model impact R 0 given a set of data. Finally, we discuss the implications of including the CTL immune response and latently infected cells in the secondary DENV infection model. Our study demonstrates that incorporating the CTL immune response and latently infected cells diminishes R 0 and enhances the system's stability around EQ 0 .

Modeling the emergence of viral resistance for SARS-CoV-2 during treatment with an anti-spike monoclonal antibody

The COVID-19 pandemic has led to over 760 million cases and 6.9 million deaths worldwide. To mitigate the loss of lives, emergency use authorization was given to several anti-SARS-CoV-2 monoclonal antibody (mAb) therapies for the treatment of mild-to-moderate COVID-19 in patients with a high risk of progressing to severe disease. Monoclonal antibodies used to treat SARS-CoV-2 target the spike protein of the virus and block its ability to enter and infect target cells. Monoclonal antibody therapy can thus accelerate the decline in viral load and lower hospitalization rates among high-risk patients with susceptible variants. However, viral resistance has been observed, in some cases leading to a transient viral rebound that can be as large as 3-4 orders of magnitude. As mAbs represent a proven treatment choice for SARS-CoV-2 and other viral infections, evaluation of treatment-emergent mAb resistance can help uncover underlying pathobiology of SARS-CoV-2 infection and may also help in the development of the next generation of mAb therapies. Although resistance can be expected, the large rebounds observed are much more difficult to explain. We hypothesize replenishment of target cells is necessary to generate the high transient viral rebound. Thus, we formulated two models with different mechanisms for target cell replenishment (homeostatic proliferation and return from an innate immune response anti-viral state) and fit them to data from persons with SARS-CoV-2 treated with a mAb. We showed that both models can explain the emergence of resistant virus associated with high transient viral rebounds. We found that variations in the target cell supply rate and adaptive immunity parameters have a strong impact on the magnitude or observability of the viral rebound associated with the emergence of resistant virus. Both variations in target cell supply rate and adaptive immunity parameters may explain why only some individuals develop observable transient resistant viral rebound. Our study highlights the conditions that can lead to resistance and subsequent viral rebound in mAb treatments during acute infection.

Mathematical modeling the dynamics of SARS-CoV-2 infection with antibody-dependent enhancement

The advent and swift global spread of the novel coronavirus (COVID-19) transmitted by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have caused massive deaths and economic devastation worldwide. Antibody-dependent enhancement (ADE) is a common phenomenon in virology that directly affects the effectiveness of the vaccine, and there is no fully effective vaccine for diseases. In order to study the potential role of ADE on SARS-CoV-2 infection, we establish the SARS-CoV-2 infection dynamics model with ADE. The basic reproduction number is computed. We prove that when R 0 < 1 , the infection-free equilibrium is globally asymptotically stable, and the system is uniformly persistent when R 0 > 1 . We carry out the sensitivity analysis by the partial rank correlation coefficients and the extended version of the Fourier amplitude sensitivity test. Numerical simulations are implemented to illustrate the theoretical results. The potential impact of ADE on SARS-CoV-2 infection is also assessed. Our results show that ADE may accelerate SARS-CoV-2 infection. Furthermore, our findings suggest that increasing antibody titers can have the ability to control SARS-CoV-2 infection with ADE, but enhancing the neutralizing power of antibodies may be ineffective to control SARS-CoV-2 infection with ADE. Our study presumably contributes to a better understanding of the dynamics of SARS-CoV-2 infection with ADE.

Theoretical Explanation for the Rarity of Antibody-Dependent Enhancement of Infection (ADE) in COVID-19

Global vaccination against the SARS-CoV-2 virus has proved to be highly effective. However, the possibility of antibody-dependent enhancement of infection (ADE) upon vaccination remains underinvestigated. Here, we aimed to theoretically determine conditions for the occurrence of ADE in COVID-19. We developed a series of mathematical models of antibody response: model Ab—a model of antibody formation; model Cv—a model of infection spread in the body; and a complete model, which combines the two others. The models describe experimental data on SARS-CoV and SARS-CoV-2 infections in humans and cell cultures, including viral load dynamics, seroconversion times and antibody concentration kinetics. The modelling revealed that a significant proportion of macrophages can become infected only if they bind antibodies with high probability. Thus, a high probability of macrophage infection and a sufficient amount of pre-existing antibodies are necessary for the development of ADE in SARS-CoV-2 infection. However, from the point of view of the dynamics of pneumocyte infection, the two cases where the body has a high concentration of preexisting antibodies and a high probability of macrophage infection and where there is a low concentration of antibodies in the body and no macrophage infection are indistinguishable. This conclusion could explain the lack of confirmed ADE cases for COVID-19.

A mathematical model to describe antibody-dependent enhancement and assess the effect of limiting cloning for plasma cells in heterologous secondary dengue infection

We propose a mathematical model to study the antibody-dependent enhancement (ADE) phenomenon. Here, we explore the interaction between macrophages, dengue virus and plasma cells, especially the effect of a limitation on plasma cell proliferation, which occurs due to immunological memory. The model has up to three equilibrium points: one virus-free equilibrium and two virus-presence equilibrium, depending on the value of two thresholds. We determine the existence regions for the model equilibrium points and their stability, a sensitivity analysis was performed in the model thresholds. Numerical simulations illustrate that ADE can occur even when the basic reproduction number is less than one.

Secondary cross infection with dengue virus serotype 2/3 aggravates vascular leakage in BALB/c mice

Dengue virus (DV) has occasionally emerged at epidemic levels in Yunnan, China. Vaccine development is limited by antibody dependent enhancement (ADE) and a lack of good animal models. Thus study investigated cross infection based on maternal immunity in BALB/c mice and assessed the risk of cross infection by DV2-D13113 and DV3-YNWS2 epidemic virus strains. DV replicated within the organs of the BALB/c infant mice, even causing death. Particularly, DV3-infected infant mice were at higher risk of severe disease if their mothers were infected with DV2. Although BALB/c adults and pups survived DV2/DV3 infection and produced anti-DV antibodies after 5-8 days, extensive subcutaneous vascular leakage was observed after secondary DV infection. Further, vascular permeability in the lung and kidney significantly increased in offspring born to heterotypic virus-infected mothers. Thus, vascular leakage indicates severe DV infection. The results indicate that maternal immunity increases the severity of subsequent heterotypic infection. Additionally, secondary cross infection by D13113 and YNWS2 represents a risk of serious disease. This study has implications for studies of DV cross infection and vaccine development. This article is protected by copyright. All rights reserved.

A mathematical model to evaluate the role of memory B and T cells in heterologous secondary dengue infection

We propose a mathematical model to investigate the antibody-dependent enhancement (ADE) phenomenon during secondary dengue infection. The model consists of an ODE system that describes the interaction of the dengue virus with macrophages and memory B and T cell role during the infection. The qualitative model analysis is done in terms of memory B and T cell cloning parameters and the basic reproduction number R₀. In the absence of memory B and T cell cloning, if R₀<1 the dengue virus population extinguishes, while for R₀>1, it tends asymptotically to a positive equilibrium. However, when we consider the memory B cell cloning, it is possible to occur dengue infection even when R₀<1. Memory T cells have an essential role in eliminating the possibility of ADE occurrence when R₀<1.

Modeling the Relationship Between Antibody-Dependent Enhancement and Disease Severity in Secondary Dengue Infection

Sequential infections with different dengue serotypes (DENV-1, 4) significantly increase the risk of a severe disease outcome (fever, shock, and hemorrhagic disorders). Two hypotheses have been proposed to explain the severity of the disease: (1) antibody-dependent enhancement (ADE) and (2) original T cell antigenic sin. In this work, we explored the first hypothesis through mathematical modeling. The proposed model reproduces the dynamic of susceptible and infected target cells and dengue virus in scenarios of infection-neutralizing and infection-enhancing antibody competition induced by two distinct serotypes of the dengue virus during secondary infection. The enhancement and neutralization functions are derived from basic concepts of chemical reactions and used to mimic binding to the virus by two distinct populations of antibodies. The analytic study of the model showed the existence of two equilibriums: a disease-free equilibrium and an endemic one. Using the concept of the basic reproduction number [Formula: see text], we performed the asymptotic stability analysis for the two equilibriums. To measure the severity of the disease, we considered the maximum value of infected cells as well as the time when this maximum is reached. We observed that it corresponds to the time when the maximum enhancing activity for the infection occurs. This critical time was calculated from the model to be a few days after the occurrence of the infection, which corresponds to what is observed in the literature. Finally, using as output [Formula: see text], we were able to rank the contribution of each parameter of the model. In particular, we highlighted that the cross-reactive antibody responses may be responsible for the disease enhancement during secondary heterologous dengue infection.

Modelling the impact of antibody-dependent enhancement on disease severity of Zika virus and dengue virus sequential and co-infection

Human infections with viruses of the genus Flavivirus, including dengue virus (DENV) and Zika virus (ZIKV), are of increasing global importance. Owing to antibody-dependent enhancement (ADE), secondary infection with one Flavivirus following primary infection with another Flavivirus can result in a significantly larger peak viral load with a much higher risk of severe disease. Although several mathematical models have been developed to quantify the virus dynamics in the primary and secondary infections of DENV, little progress has been made regarding secondary infection of DENV after a primary infection of ZIKV, or DENV-ZIKV co-infection. Here, we address this critical gap by developing compartmental models of virus dynamics. We first fitted the models to published data on dengue viral loads of the primary and secondary infections with the observation that the primary infection reaches its peak much more gradually than the secondary infection. We then quantitatively show that ADE is the key factor determining a sharp increase/decrease of viral load near the peak time in the secondary infection. In comparison, our simulations of DENV and ZIKV co-infection (simultaneous rather than sequential) show that ADE has very limited influence on the peak DENV viral load. This indicates pre-existing immunity to ZIKV is the determinant of a high level of ADE effect. Our numerical simulations show that (i) in the absence of ADE effect, a subsequent co-infection is beneficial to the second virus; and (ii) if ADE is feasible, then a subsequent co-infection can induce greater damage to the host with a higher peak viral load and a much earlier peak time for the second virus, and for the second peak for the first virus.