A Novel Study of Tumor-Immune-Microbiome with Cost Effective Analysis

Abstract

The complex interplay among tumor cells, immune cells, and the microbiome has recently gained attention as a crucial determinant of cancer growth and treatment outcomes. In this work, a mathematical model has been developed and analysed to capture tumor-immune-microbiome interactions using a system of ordinary differential equations. It is explored how microbial species influence immune response and tumor growth dynamics. Applied analytical techniques reveal critical thresholds that govern tumor persistence. Moreover, an optimal control problem has been formulated, yielding effective therapeutic strategies that balance immune activation and microbiome modulation at the lowest treatment cost. The integrated approach provides novel insights into the mathematical foundation of the cancer-immune-microbiome system and explores sophisticated avenues for optimized cancer therapy.