Dynamical demeanour of SARS-CoV-2 virus undergoing immune response mechanism in COVID-19 pandemic

Within-host dynamics of HTLV-2 and HIV-1 co-infection with delay

This paper formulates a mathematical model for the co-infection of HTLV-2 and HIV-1 with latent reservoirs, four types of distributed-time delays and HIV-1-specific B cells. We establish that the solutions remain bounded and nonnegative, identify the system's steady states, and derive sufficient conditions ensuring both their existence and global asymptotic stability. The system's global stability is confirmed using Lyapunov's method. We provide numerical simulations to support the stability results. Sensitivity analysis of basic reproduction numbers of HTLV-2 mono-infection (R 1 ) and HIV-1 mono-infection (R 2 ) is conducted. We examine how time delays influence the interaction between HIV-1 and HTLV-2. Including delay terms in the model reflects the influence of antiviral treatments, which help decrease R 1 and R 2 , thus limiting the spread of infection. This highlights the potential for designing therapies that prolong delay period. Incorporating such delays improves model precision and supports more effective evaluation of treatment strategies.

Stability of a discrete HTLV-1/SARS-CoV-2 dual infection model

Dual infection with a virus that targets the immune system, such as HTLV-1 (human T-cell lymphotropic virus class 1), combined with another virus that affects the respiratory system, such as SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), can cause serious disease and even death. Given the significance of better comprehending the dual viral infections' dynamics, researchers have been drawn to mathematical analyses of such models. This work investigates the stability of a discrete HTLV-1/SARS-CoV-2 dual infection model. Our approach involves formulating the discrete model through the discretization of the continuous-time one using NSFD (nonstandard finite difference) method. We demonstrate that the NSFD method preserves essential properties of the solutions, such as positivity and boundedness. Additionally, we determine the fixed points and establish the conditions under which they exist. Furthermore, we analyze the global stability of these fixed points utilizing the Lyapunov technique. To illustrate our analytical findings, we do numerical simulations.

The spatial dynamics of immune response upon virus infection through hybrid dynamical computational model

Introduction

The immune responses play important roles in the course of disease initiation and progression upon virus infection such as SARS-CoV-2. As the tissues consist of spatial structures, the spatial dynamics of immune responses upon viral infection are essential to the outcome of infection.

Methods

A hybrid computational model based on cellular automata coupled with partial differential equations is developed to simulate the spatial patterns and dynamics of the immune responses of tissue upon virus infection with several different immune movement modes.

Results

Various patterns of the distribution of virus particles under different immune strengths and movement modes of immune cells are obtained through the computational models. The results also reveal that the directed immune cell wandering model has a better immunization effect. Several other characteristics, such as the peak level of virus density and onset time and the onset of the diseases, are also checked with different immune and physiological conditions, for example, different immune clearance strengths, and different cell-to-cell transmission rates. Furthermore, by the Lasso analysis, it is identified that the three main parameters had the most impact on the rate of onset time of disease. It is also shown that the cell-to-cell transmission rate has a significant effect and is more important for controlling the diseases than those for the cell-free virus given that the faster cell-to-cell transmission than cell-free transmission the rate of virus release is low.

Discussion

Our model simulates the process of viral and immune response interactions in the alveola repithelial tissues of infected individuals, providing insights into the viral propagation of viruses in two dimensions as well as the influence of immune response patterns and key factors on the course of infection.

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response

This paper develops and analyzes a SARS-CoV-2 dynamics model with logistic growth of healthy epithelial cells, CTL immune and humoral (antibody) immune responses. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. We deduce that the model has five steady states and their existence and stability are perfectly determined by four threshold parameters. We study the global stability of the model's steady states using Lyapunov method. The analytical results are enhanced by numerical simulations. The impact of intracellular time delays on the dynamical behavior of the SARS-CoV-2 is addressed. We noted that increasing the time delay period can suppress the viral replication and control the infection. This could be helpful to create new drugs that extend the delay time period.

Global dynamics of IAV/SARS-CoV-2 coinfection model with eclipse phase and antibody immunity

Coronavirus disease 2019 (COVID-19) and influenza are two respiratory infectious diseases of high importance widely studied around the world. COVID-19 is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), while influenza is caused by one of the influenza viruses, A, B, C, and D. Influenza A virus (IAV) can infect a wide range of species. Studies have reported several cases of respiratory virus coinfection in hospitalized patients. IAV mimics the SARS-CoV-2 with respect to the seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the within-host dynamics of IAV/SARS-CoV-2 coinfection with the eclipse (or latent) phase. The eclipse phase is the period of time that elapses between the viral entry into the target cell and the release of virions produced by that newly infected cell. The role of the immune system in controlling and clearing the coinfection is modeled. The model simulates the interaction between nine compartments, uninfected epithelial cells, latent/active SARS-CoV-2-infected cells, latent/active IAV-infected cells, free SARS-CoV-2 particles, free IAV particles, SARS-CoV-2-specific antibodies and IAV-specific antibodies. The regrowth and death of the uninfected epithelial cells are considered. We study the basic qualitative properties of the model, calculate all equilibria, and prove the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. The theoretical findings are demonstrated via numerical simulations. The importance of considering the antibody immunity in the coinfection dynamics model is discussed. It is found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence will not occur. Further, we discuss the effect of IAV infection on the dynamics of SARS-CoV-2 single infection and vice versa.

Dynamics of the COVID-19 pandemic: nonlinear approaches on the modelling, prediction and control

This special issue contains 35 regular articles on the analysis and dynamics of COVID-19 with several applications. Some analyses are on the construction of mathematical models representing the dynamics of COVID-19, and some are on the estimations and predictions of the disease, a few with possible applications. The various contributions report important, timely, and promising results, such as the effects of several waves, deep learning-based COVID-19 classifications, and multivariate time series with applications.

Clinical effects of 2-DG drug restraining SARS-CoV-2 infection: A fractional order optimal control study

Fractional calculus is very convenient tool in modeling of an emergent infectious disease system comprising previous disease states, memory of disease patterns, profile of genetic variation etc. Significant complex behaviors of a disease system could be calibrated in a proficient manner through fractional order derivatives making the disease system more realistic than integer order model. In this study, a fractional order differential equation model is developed in micro level to gain perceptions regarding the effects of host immunological memory in dynamics of SARS-CoV-2 infection. Additionally, the possible optimal control of the infection with the help of an antiviral drug, viz. 2-DG, has been exemplified here. The fractional order optimal control would enable to employ the proper administration of the drug minimizing its systematic cost which will assist the health policy makers in generating better therapeutic measures against SARS-CoV-2 infection. Numerical simulations have advantages to visualize the dynamical effects of the immunological memory and optimal control inputs in the epidemic system.

Timely and effective media coverage's role in the spread of Corona Virus Disease 2019

For all humanity, the sudden outbreak of Corona Virus Disease 2019 has been an important problem. Timely and effective media coverage is considered to be one of the effective approaches to control the spread of epidemic in early stage. In this paper, a Sentiment-enabled Susceptible-Exposed-Infected-Recovered (SEIR) model is established to reveal the relationship between the propagation of the epidemic and media coverage. The authors take the positive and negative media coverage into consideration when implementing the Sentiment-enabled SEIR model. This model is constructed by parameterizing the number of current confirmed cases, cumulative cured cases, cumulative deaths, and media coverage. The numerical simulation and sensitivity analysis are conducted based on the Sentiment-enabled SEIR model. The numerical analysis confirms the rationality of the Sentiment-enabled SEIR model. The sensitivity analysis shows that positive media coverage acts a pivotal part in reducing the figure for confirmed cases. Negative media coverage has an effect on the figure for confirmed cases is not as significant as that of positive media coverage, but it is not negligible.

Global Stability of a Humoral Immunity COVID-19 Model with Logistic Growth and Delays

The mathematical modeling and analysis of within-host or between-host coronavirus disease 2019 (COVID-19) dynamics are considered robust tools to support scientific research. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. This paper proposes and investigates a within-host COVID-19 dynamics model with latent infection, the logistic growth of healthy epithelial cells and the humoral (antibody) immune response. Time delays can affect the dynamics of SARS-CoV-2 infection predicted by mathematical models. Therefore, we incorporate four time delays into the model: (i) delay in the formation of latent infected epithelial cells, (ii) delay in the formation of active infected epithelial cells, (iii) delay in the activation of latent infected epithelial cells, and (iv) maturation delay of new SARS-CoV-2 particles. We establish that the model’s solutions are non-negative and ultimately bounded. This confirms that the concentrations of the virus and cells should not become negative or unbounded. We deduce that the model has three steady states and their existence and stability are perfectly determined by two threshold parameters. We use Lyapunov functionals to confirm the global stability of the model’s steady states. The analytical results are enhanced by numerical simulations. The effect of time delays on the SARS-CoV-2 dynamics is investigated. We observe that increasing time delay values can have the same impact as drug therapies in suppressing viral progression. This offers some insight useful to develop a new class of treatment that causes an increase in the delay periods and then may control SARS-CoV-2 replication.

Early Prediction Model for Critical Illness of Hospitalized COVID-19 Patients Based on Machine Learning Techniques

Motivation

Patients with novel coronavirus disease 2019 (COVID-19) worsen into critical illness suddenly is a matter of great concern. Early identification and effective triaging of patients with a high risk of developing critical illness COVID-19 upon admission can aid in improving patient care, increasing the cure rate, and mitigating the burden on the medical care system. This study proposed and extended classical least absolute shrinkage and selection operator (LASSO) logistic regression to objectively identify clinical determination and risk factors for the early identification of patients at high risk of progression to critical illness at the time of hospital admission.

Methods

In this retrospective multicenter study, data of 1,929 patients with COVID-19 were assessed. The association between laboratory characteristics measured at admission and critical illness was screened with logistic regression. LASSO logistic regression was utilized to construct predictive models for estimating the risk that a patient with COVID-19 will develop a critical illness.

Results

The development cohort consisted of 1,363 patients with COVID-19 with 133 (9.7%) patients developing the critical illness. Univariate logistic regression analysis revealed 28 variables were prognosis factors for critical illness COVID-19 (p < 0.05). Elevated CK-MB, neutrophils, PCT, α-HBDH, D-dimer, LDH, glucose, PT, APTT, RDW (SD and CV), fibrinogen, and AST were predictors for the early identification of patients at high risk of progression to critical illness. Lymphopenia, a low rate of basophils, eosinophils, thrombopenia, red blood cell, hematocrit, hemoglobin concentration, blood platelet count, and decreased levels of K, Na, albumin, albumin to globulin ratio, and uric acid were clinical determinations associated with the development of critical illness at the time of hospital admission. The risk score accurately predicted critical illness in the development cohort [area under the curve (AUC) = 0.83, 95% CI: 0.78-0.86], also in the external validation cohort (n = 566, AUC = 0.84).

Conclusion

A risk prediction model based on laboratory findings of patients with COVID-19 was developed for the early identification of patients at high risk of progression to critical illness. This cohort study identified 28 indicators associated with critical illness of patients with COVID-19. The risk model might contribute to the treatment of critical illness disease as early as possible and allow for optimized use of medical resources.