Analysis of a deterministic-stochastic oncolytic M1 model involving immune response via crossover behaviour: ergodic stationary distribution and extinction

Oncolytic virotherapy is a viable chemotherapeutic agent that identifies and kills tumor cells using replication-competent pathogens. Oncolytic alphavirus M1 is a naturally existing disease that has been shown to have rising specificity and potency in cancer progression. The objective of this research is to introduce and analyze an oncolytic M1 virotherapy framework with spatial variability and anti-tumor immune function via piecewise fractional differential operator techniques. To begin, we potentially demonstrate that the stochastic system's solution is non-negative and global by formulating innovative stochastic Lyapunov candidates. Then, we derive the existence-uniqueness of an ergodic stationary distribution of the stochastic framework and we establish a sufficient assumption RP0 < 1 extermination of tumor cells and oncolytic M1 virus. Using meticulous interpretation, this model allows us to analyze and anticipate the procedure from the start to the end of the tumor because it allows us to examine a variety of behaviours ranging from crossover to random mechanisms. Furthermore, the piecewise differential operators, which can be assembled with operators including classical, Caputo, Caputo-Fabrizio, Atangana-Baleanu, and stochastic derivative, have decided to open up innovative avenues for readers in various domains, allowing them to encapsulate distinct characteristics in multiple time intervals. Consequently, by applying these operators to serious challenges, scientists can accomplish better outcomes in documenting facts.