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Piecewise differentiation of the fractional order CAR-T cells-SARS-2 virus model
Ayesha Sohail1, Zhenhua Yu2, Robia Arif1
1Department of Mathematics, Comsats University Islamabad, Lahore 54000, Pakistan.
Abstract:
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.
Insights
This study explores using CAR-T cell immunotherapy, a cancer treatment, to combat SARS-CoV-2. A mathematical model supports the hypothesis that CAR-T cells can effectively target and eliminate the virus causing COVID-19.
Area of Science:
- Immunology
- Virology
- Mathematical Biology
Background:
- The COVID-19 pandemic necessitates novel therapeutic strategies.
- Immunotherapy, particularly CAR-T cell technology, has shown promise against viral infections like HIV.
- CAR-T cells offer potential for treating viral diseases by targeting infected cells.
Purpose of the Study:
- To hypothesize and mathematically model the application of CAR-T cell immunotherapy against SARS-CoV-2.
- To investigate the feasibility of adapting CAR technology for COVID-19 treatment.
- To analyze the interactions between CAR-T cells, memory cells, and SARS-CoV-2 infected cells.
Main Methods:
- Development of a mathematical model using fractional calculus (Caputo derivative).
- Analysis of the existence and non-negativity of solutions within the mathematical model.
- Application of piecewise derivatives and Newton polynomial interpolation for further validation.
Main Results:
- The mathematical model provides evidence supporting the hypothesis of CAR-T cell efficacy against SARS-CoV-2.
- Analysis confirmed the stability and non-negativity of the model's solutions.
- The study demonstrates the potential of adapting CAR-T cell therapy for viral infections.
Conclusions:
- CAR-T cell immunotherapy presents a viable therapeutic avenue for COVID-19.
- Mathematical modeling is a valuable tool for exploring novel therapeutic strategies.
- Further research into CAR-T cell adaptation for SARS-CoV-2 is warranted.
