A SEIQRD EPIDEMIC MODEL TO STUDY THE DYNAMICS OF COVID-19 DISEASE

In this paper, we propose a COVID-19 epidemic model with quarantine class. The model contains 6 sub-populations, namely the susceptible (S), exposed (E), infected (I), quarantined (Q), recovered (R), and death (D) sub-populations. For the proposed model, we show the existence, uniqueness, non-negativity, and boundedness of solution. We obtain two equilibrium points, namely the disease-free equilibrium (DFE) point and the endemic equilibrium (EE) point. Applying the next generation matrix, we get the basic reproduction number (R0). It is found that R0 is inversely proportional to the quarantine rate as well as to the recovery rate of infected subpopulation. The DFE point always exists and if R0 < 1 then the DFE point is asymptotically stable, both locally and globally. On the other hand, if R0 > 1 then there exists an EE point, which is globally asymptotically stable. Here, there occurs a forward bifurcation driven by R0 . The dynamical properties of the proposed model have been verified our numerical simulations. © 2023 the author(s).

A SEIQRD EPIDEMIC MODEL TO STUDY THE DYNAMICS OF COVID-19 DISEASE

In this paper, we propose a COVID-19 epidemic model with quarantine class. The model contains 6 sub-populations, namely the susceptible (S), exposed (E), infected (I), quarantined (Q), recovered (R), and death (D) sub-populations. For the proposed model, we show the existence, uniqueness, non-negativity, and boundedness of solution. We obtain two equilibrium points, namely the disease-free equilibrium (DFE) point and the endemic equilibrium (EE) point. Applying the next generation matrix, we get the basic reproduction number (R0). It is found that R0 is inversely proportional to the quarantine rate as well as to the recovery rate of infected subpopulation. The DFE point always exists and if R0 < 1 then the DFE point is asymptotically stable, both locally and globally. On the other hand, if R0 > 1 then there exists an EE point, which is globally asymptotically stable. Here, there occurs a forward bifurcation driven by R0 . The dynamical properties of the proposed model have been verified our numerical simulations. © 2023 the author(s).

Pattern formation induced by fractional-order diffusive model of COVID-19

Differential equations with complex order fractional derivatives enable the regulation of complicated fractional systems. Within this scale, fractional calculus unfolds the fundamental mechanisms and multi-scale dynamic phenomena in biological tissues. It is viable that weakly nonlinear analysis represents a system that includes amplitude equations and the analysis that corresponds with it, which allows the prediction of the various patterns of parameter regimes likely to coexist in complicated dynamical and transient circumstances. A weakly nonlinear analysis creates a system comprising amplitude equations in dynamical contexts with fractional-order system characteristics, and its associated analyses are useful for predicting parameter regimes of several patterns that are expected to coexist. The development of patterns as a result of Turing instability in the homogeneous steady state is known to be a Turing process addressing unpredictability in numerous contexts. In a COVID-19 model, we investigate the Turing instability produced by fractional diffusion. To that purpose, positive equilibrium points are first specified, and then the Routh-Hurwitz criteria are used to assess the positive equilibrium point's stability. Local equilibrium points and stability analysis are employed to find the conditions for Turing instability. The amplitude equations near the Turing bifurcation point are deduced using weakly nonlinear analysis. After the application of amplitude equations, this structure has manifested highly rich dynamical properties. Regarding the amplitude equations, the dynamic analysis determines the conditions for the development of patterns such as spot, hexagon, stripe, and mixed patterns. Moreover, the theoretical effects are confirmed using numerical simulations. Within this context, this analysis, which looks into the system's dynamical behavior and the bifurcation point centered on the death rate, will serve as a leverage for further studies in different disciplines concerning COVID-19 model through the lenses of distinct viewpoints. Based on modeling as regards complex and heterogeneous materials, fractional system ensures the formation of patterns by identifying the specific and required significant attributes of complexity that convey information in terms of dynamical behavior. As a result of the analyses which reveal the highly complex connection between COVID-19 and fractional-order diffusion, the Turing bifurcation point and weakly nonlinear analysis used in the fractional-order dynamics discussed in this study are critically important on a quantitative basis owing to the fact that the results can be applied and extended to a variety of statistical, physical, engineering, biological and other related further models. © 2022 Elsevier Inc. All rights reserved.

Modeling the crossover behavior of the bacterial infection with the COVID-19 epidemics.

To explore the crossover linkage of the bacterial infections resulting from the viral infection, within the host body, a computational framework is developed. It analyzes the additional pathogenic effect of Streptococcus pneumonia, one of the bacteria that can trigger the super-infection mechanism in the COVID-19 syndrome and the physiological effects of innate immunity for the control or eradication of this bacterial infection. The computational framework, in a novel manner, takes into account the action of pro-inflammatory and anti-inflammatory cytokines in response to the function of macrophages. A hypothetical model is created and is transformed to a system of non-dimensional mathematical equations. The dynamics of three main parameters (macrophages sensitivity κ , sensitivity to cytokines η and bacterial sensitivity ϵ ), analyzes a "threshold value" termed as the basic reproduction number R 0 which is based on a sub-model of the inflammatory state. Piece-wise differentiation approach is used and dynamical analysis for the inflammatory response of macrophages is studied in detail. The results shows that the inflamatory response, with high probability in bacterial super-infection, is concomitant with the COVID-19 infection. The mechanism of action of the anti-inflammatory cytokines is discussed during this research and it is observed that these cytokines do not prevent inflammation chronic, but only reduce its level while increasing the activation threshold of macrophages. The results of the model quantifies the probable deficit of the biological mechanisms linked with the anti-inflammatory cytokines. The numerical results shows that for such mechanisms, a minimal action of the pathogens is strongly amplified, resulting in the "chronicity" of the inflammatory process.

Piecewise differentiation of the fractional order CAR-T cells-SARS-2 virus model.

The pandemic caused by the SARS-CoV2 virus has prompted research into new therapeutic solutions that can be used to treat the CoVid-19 syndrome. As part of this research, immunotherapy, first developed against cancer, is offering new therapeutic horizons also against viral infections. CAR technology, with the production of CAR-T cells (adoptive immunotherapy), has shown applicability in the field of HIV viral infections through second generation CAR-T cells implemented with the "CD4CAR" system with a viral fusion inhibitor. In addition, to avoid the immunoescape of the virus, bi- or trispecific CAR receptors have been developed. Our research group hypothesizes the use of this immunotherapy system against SARS-CoV2, admitting the appropriate adjustments concerning the target-epitope and a possible remodeling of the nuclease related to the action of this virus. For a more in-depth analysis of this hypothesis, a mathematical model has been developed which, starting from the fractional derivative Caputo, creates a system of equations that describes the interactions between CAR-T cells, memory cells, and cells infected with SARS-CoV2. Through an analysis of the existence and non-negativity of the solutions, the hypothesis is stabilized; then is further demonstrated through the use of the piece-wise derivative and the consequent application of the formula of Newton polynomial interpolation.

Self organizing maps for the parametric analysis of COVID-19 SEIRS delayed model.

Since 2019, entire world is facing the accelerating threat of Corona Virus, with its third wave on its way, although accompanied with several vaccination strategies made by world health organization. The control on the transmission of the virus is highly desired, even though several key measures have already been made, including masks, sanitizing and disinfecting measures. The ongoing research, though devoted to this pandemic, has certain flaws, due to which no permanent solution has been discovered. Currently different data based studies have emerged but unfortunately, the pandemic fate is still unrevealed. During this research, we have focused on a compartmental model, where delay is taken into account from one compartment to another. The model depicts the dynamics of the disease relative to time and constant delays in time. A deep learning technique called "Self Organizing Map" is used to extract the parametric values from the data repository of COVID-19. The input we used for SOM are the attributes on which, the variables are dependent. Different grouping/clustering of patients were achieved with 2- dimensional visualization of the input data ( h t t p s : / / c r e a t i v e c o m m o n s . o r g / l i c e n s e s / b y / 2.0 / ). Extensive stability analysis and numerical results are presented in this manuscript which can help in designing control measures.

Delayed Modeling Approach to Forecast the Periodic Behavior of SARS-2.

The ongoing threat of Coronavirus is alarming. The key players of this virus are modeled mathematically during this research. The transmission rates are hypothesized, with the aid of epidemiological concepts and recent findings. The model reported is extended, by taking into account the delayed dynamics. Time delay reflects the fact that the dynamic behavior of transmission of the disease, at time t depends not only on the state at time t but also on the state in some period τ before time t. The research presented in this manuscript will not only help in understanding the current threat of pandemic (SARS-2), but will also contribute in making precautionary measures and developing control strategies.

Forecasting the timeframe of 2019-nCoV and human cells interaction with reverse engineering.

In December 2019, an atypical pneumonia invaded the city of Wuhan, China, and the causative agent of this disease turned out to be a new coronavirus. In January 2020, the World Health Organization named the new coronavirus 2019-nCoV and subsequently it is referred to as SARS-CoV2 and the related disease as CoViD-19 (Lai et al., 2020). Very quickly, the epidemic led to a pandemic and it is now a worldwide emergency requiring the creation of new antiviral therapies and a related vaccine. The purpose of this article is to review and investigate further the molecular mechanism by which the SARS-CoV2 virus infection proceeds via the formation of a hetero-trimer between its protein S, the ACE2 receptor and the B0AT1 protein, which is the "entry receptor" for the infection process involving membrane fusion (Li et al., 2003). A reverse engineering process uses the formalism of the Hill function to represent the functions related to the dynamics of the biochemical interactions of the viral infection process. Then, using a logical evaluation of viral density that measures the rate at which the cells are hijacked by the virus (and they provide a place for the virus to replicate) and considering the "time delay" given by the interaction between cell and virus, the expected duration of the incubation period is predicted. The conclusion is that the density of the virus varies from the "exposure time" to the "interaction time" (virus-cells). This model can be used both to evaluate the infectious condition and to analyze the incubation period. BACKGROUND: The ongoing threat of the new coronavirus SARS-CoV2 pandemic is alarming and strategies for combating infection are highly desired. This RNA virus belongs to the ß-coronavirus genus and is similar in some features to SARS-CoV. Currently, no vaccine or approved medical treatment is available. The complex dynamics of the rapid spread of this virus can be demonstrated with the aid of a computational framework. METHODS: A mathematical model based on the principles of cell-virus interaction is developed in this manuscript. The amino acid sequence of S proein and its interaction with the ACE-2 protein is mimicked with the aid of Hill function. The mathematical model with delay is solved with the aid of numerical solvers and the parametric values are obtained with the help of MCMC algorithm. RESULTS: A delay differential equation model is developed to demonstrate the dynamics of target cells, infected cells and the SARS-CoV2. The important parameters and coefficients are demonstrated with the aid of numerical computations. The resulting thresholds and forecasting may prove to be useful tools for future experimental studies and control strategies. CONCLUSIONS: From the analysis, I is concluded that control strategy via delay is a promising technique and the role of Hill function formalism in control strategies can be better interpreted in an inexpensive manner with the aid of a theoretical framework.