👉 Mathematical infection, often conceptualized through epidemiological models, describes the spread of an infectious disease within a population using mathematical equations to predict how quickly and extensively the disease will propagate. At its core, this concept is typically modeled using differential equations, such as the SIR (Susceptible-Infected-Recovered) model, which divides the population into three compartments: Susceptible (S), Infected (I), and Recovered (R). The dynamics of these compartments are governed by rates of infection and recovery. The infection rate, often denoted as β (beta), represents how frequently susceptible individuals become infected by infected ones, while the recovery rate, denoted as γ (gamma), indicates how quickly infected individuals recover and move to the recovered state. The basic reproduction number, R₀, is a critical threshold value that determines whether an infection will spread (R₀ > 1) or die out (R₀ < 1). Mathematically, the infection process can be described by the equation dS/dt = -βSI/N, dI/dt = βSI/N - γI, and dR/dt = γI, where N is the total population size. These equations illustrate how the number of infected individuals grows until the recovery rate balances the infection rate, leading to a dynamic equilibrium or exponential growth, depending on the initial conditions and parameters.
