Non-invasive methods for monitoring the condition of laboratory animals play a key role in ensuring animal welfare and improving the reliability of scientific data. This study evaluates the effectiveness of two non-invasive approaches - daily body weight measurement and urine analysis by qPCR - for monitoring the health of BALB/c mice infected with tick-borne encephalitis virus (TBEV). Calculation of the first derivative of body weight change allowed precise determination of disease onset, which correlated with clinical symptoms and detection of viral RNA in urine. Mathematical analysis of body weight change dynamics (first derivative with type 2 cubic spline smoothing, rh = 1) showed that a derivative threshold value of ≤ −0.6 reliably distinguishes infected BALB/c mice from healthy ones (AUC = 1 in ROC analysis). Urine analysis by qPCR allowed for the detection of viral RNA as early as the second day after infection, with a peak on the seventh day. The mathematical model was further tested on C57BL/6, CBA, and BALB/c mice of different ages and proved to be suitable. The threshold values of the derivative were found to be dependent on the mouse strain. The proposed non-invasive methods offer a humane and accurate alternative to invasive procedures, contributing to higher ethical standards and quality of research in virology.