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Fibroblast cells are involved in the mechanism of growth and repair of tissue in human organs. Calcium (Ca2+) signaling is essentially required to maintain the microstructure and physiological function of the fibroblast cell. The study of Ca2+ signaling in fibroblast cells is crucial to understanding the mechanisms and disorders of fibroblast cells. The inositol 1,4,5- trisphosphate (IP3) participates in the release and extension of calcium from the endoplasmic reticulum (ER). Adenosine triphosphate (ATP) also regulate various biological activity like proliferation, migration, stimulation of cell growth, etc. Any disturbance in Ca2+ can disturb the levels of IP3 and ATP in the cell. The Ca2+ dynamics and its relationship with IP3 and ATP production are not well understood. There is a need to understand the relationship among various parameters of Ca2+ dynamics and its role in IP3 and ATP production. The Ca2+ dynamics in fibroblast have been investigated by several researchers, but no attention is reported for analyzing Ca2+ dynamic production of IP3 and ATP. A mathematical model is proposed for analyzing the role of Ca2+ signaling in the production of IP3 and ATP in fibroblast cells. The model incorporates the effect of diffusion, buffer, leak, sarco endoplasmic reticulum calcium ATPase (SERCA) pump, etc. The model is formulated in the form of an initial-boundary problem. The solution is obtained using the finite element approach. The effects of excessive or low values of various parameters on Ca2+ dynamics, ATP production, IP3 production, and IP3 degradation have been analyzed for possible disorders in functions of a fibroblast cell. The alterations in these parameters cause alterations in ATP production, IP3 production and IP3 degradation and Ca2+ concentration profiles. This alteration in parameters can be responsible for the function and dysfunction of fibroblast cells, leading to cardiac disease, fibrosis, delayed wound healing, etc. The results lead to conclusion that the changes in source influx, buffers, and diffusion coefficient can cause an increase or decrease in ATP and IP3 production and IP3 degradation leading to disorders of fibroblast cells like cardiac fibroblast cell proliferation and migration, which have a role in wound healing, inflammation, and cancer . Obtained results provide insights into the Ca2+-dependent production of IP3 and ATP in a fibroblast cell. These insights can be useful for developing diagnostics and treating disorders of fibroblast cells.