Mathematics can be divided into two main categories: applied mathematics and fundamental or theoretical mathematics. Special functions have contributed and continue to contribute to the advancement of science in general and mathematics in particular. Among these functions are the Laplace transform, the Riemann zeta function, the basic reproduction number $R_{0}$, the Fourier transform, the Stieljest integral, the Lebesgue integral, $\cdots$. All these functions have made it possible, at crucial moments in the history of mathematics, to solve linear and nonlinear partial differential equations, cryptography, number theory, $\cdots$.\\ In this paper, we construct a special function $\Phi_{m}$ depending on the parameter $R_{0}$ and the independent vector $x\in\mathbb{R}^{m}$ of size $m\in\mathbb{N}^{\ast}$. The basic reproduction number $R_{0}$ is by definition the average number of new infections in an environment from an already infected individual. In other words, based on an infected individual, the $R_{0}$ provides information on the average number of people that individual can infect in a healthy environment. This number does not take into account the nature of the disease, the patient's genetic material or immune system, their family tree, or herd immunity. Through this special function $\Phi_{m}$, we propose to take into account additional parameters that are much more realistic and adapted to physical realities. The independent variable $x$ is of dimension $m\in\mathbb{N}^{\ast}$, i.e., $x=(x_{1},x_{2},\cdots,x_{m})\in\mathbb{R}^{m}$, and the dependent variable $\Phi_{m}(R_{0},x)$ is the special function. We first justify that the special function constructed is well defined. We then propose a qualitative analysis (continuity, differentiability, metric space, $\cdots$) of this special function. Finally, we propose a conceptual framework for applying this special function to the mathematical modeling of the interactive dynamics of three entities: the immune system, drugs, and nutrition.