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.

Furin and the adaptive mutation of SARS-COV2: a computational framework.

SARS-2 virus has reached its most harmful mutated form and has damaged the world's economy, integrity, health system and peace to a limit. An open problem is to address the release of antibodies after the infection and after getting the individuals vaccinated against the virus. The viral fusion process is linked with the furin enzyme and the adaptation is linked with the mutation, called D614G mutation. The cell-protein studies are extremely challenging. We have developed a mathematical model to address the process at the cell-protein level and the delay is linked with this biological process. Genetic algorithm is used to approximate the parametric values. The mathematical model proposed during this research consists of virus concentration, the infected cells count at different stages and the effect of interferon. To improve the understanding of this model of SARS-CoV2 infection process, the action of interferon (IFN) is quantified using a variable for the non-linear mathematical model, that is based on a degradation parameter γ . This parameter is responsible for the delay in the dynamics of this viral action. We emphasize that this delay responds to the evasion by SARS-CoV2 via antagonizing IFN production, inhibiting IFN signaling and improving viral IFN resistance. We have provided videos to explain the modeling scheme.

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.

Forecasting of the efficiency of monoclonal therapy in the treatment of CoViD-19 induced by the Omicron variant of SARS-CoV2.

On November 26, 2021, the World Health Organization (WHO) announced a new variant of concern of SARS-CoV2 called Omicron. This variant has biological-functional characteristics such as to make it much faster in the infectious process so as to show an even more intense spread. Although many data are currently incomplete, it is possible to identify, based on the viral biochemical characteristics, a possible therapy consisting of a monoclonal antibody called Sotrovimab. The model proposed here is based on the mathematical analysis of the dynamics of action of this monoclonal antibody and two cell populations: the immune memory cells and the infected cells. Indeed, a delay exists during the physiological immune response and the response induced by administration of Sotrovimab. This manuscript presents that delay in a novel manner. The model is developed with the aid of information based on the chemical kinetics. The machine learning tools have been used to satisfy the criteria designed by the dynamical analysis. Regression learner tools of Python are used as the reverse engineering tools for the understanding of the balance in the mathematical model, maintained by the parameters and their corresponding intervals and thresholds set by the dynamical analysis.

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.

Forecasting the action of CAR-T cells against SARS-corona virus-II infection with branching process.

The CAR-T cells are the genetically engineered T cells, designed to work specifically for the virus antigens (or other antigens, such as tumour specific antigens). The CAR-T cells work as the living drug and thus provides an adoptive immunotherapy strategy. The novel corona virus treatment and control designs are still under clinical trials. One of such techniques is the injection of CAR-T cells to fight against the COVID-19 infection. In this manuscript, the hypothesis is based on the CAR-T cells, that are suitably engineered towards SARS-2 viral antigen, by the N protein. The N protein binds to the SARS-2 viral RNA and is found in abundance in this virus, thus for the engineered cell research, this protein sequence is chosen as a potential target. The use of the sub-population of T-reg cells is also outlined. Mathematical modeling of such complex line of action can help to understand the dynamics. The modeling approach is inspired from the probabilistic rules, including the branching process, the Moran process and kinetic models. The Moran processes are well recognized in the fields of artificial intelligence and data science. The model depicts the infectious axis "virus-CAR-T cells-memory cells". The theoretical analysis provides a positive therapeutic action; the delay in viral production may have a significant impact on the early stages of infection. Although it is necessary to carefully evaluate the possible side effects of therapy. This work introduces the possibility of hypothesizing an antiviral use by CAR-T cells.

Computational model to explore the endocrine response to trastuzumab action in HER-2/neu positive breast cancer.

Breast cancer is a very frequent type of cancer and much attention is paid to therapy with considerable efforts both in the pharmacological and clinical fields.The present work aims to create a non-linear dynamic model of action of the drug Trastuzumab against HER-2 + breast cancer, mainly considering its action of ADCP (antibody-dependent phagocytosis) killing of cancer cells. The model, while also considering the other therapeutic effects induced by Trastuzumab, shows how the action of this monoclonal antibody in the induction of ADCP through the action of macrophages, is strictly connected to the formation of a multi-complex "Trastuzumab -HER-2 - macrophage" that shows a prolonged action over time, responsible for the increase in the Overall Survivor (OS) parameter reported in various. The model shows the correlation between the various therapeutic effects and the killing action of cancer cells through the variation of the dynamic fluctuation of the representative "c" parameter.

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.