## 3 Results and Discussion  
All actual values of the database were dimensionless (by dividing the value of each column by the maximum value of the same column). Dimensionless values bring all values to the interval from zero to one. This procedure makes the equation less rigid and simplifies the computational process. In this paper, all values were dimensionless. Pearson's correlation coefficients were calculated according to Formula (1), which characterize the strength of the relationship between the parameters (\(\leq\)1). The results of calculating the correlation between the biomarkers and social characteristics of respondents are shown in Figures 2-4:  
Figure 2: Pearson correlation coefficients for respondents aged 65–74. From the correlation plots (see Figures 2-4), we determined the best relationships between biomarkers and social characteristics of respondents to show the level of interaction between the product of parameters in Equations (2)-(4) as shown in Table 1.  
Figure 4: Pearson correlation coefficients for respondents aged 90 and above. Figure 3: Pearson correlation coefficients for respondents aged 75–89. We developed a mathematical model in the form of a nonlinear dynamic (nonstationary) equation that could provide a prediction of changes in premature aging. For patients in the age range of 65-74 years, we mathematically assumed that their cardiovascular system aged as follows:  
\[\frac{dx}{dt}=a_{1}\cdot Px(x,t)\cdot S(x,t)+b_{1}\cdot Px(x,t)\cdot A(x,t)+c_{1 }\cdot I(x,t)\cdot S(x,t)+d_{1}\cdot Pr(x,t)\cdot S(x,t), \tag{2}\]  
where the total derivative \(\frac{dx}{dt}\) in the left part of Equation (2) represents the process of premature ageing by time \(t\). The first term is the interaction of postinfarction cardiosclerosis and smoking, the second term postinfarction cardiosclerosis and alcohol, the third term body mass index with smoking, and the fourth term blood pressure with smoking, respectively, with probabilities \(a_{1}\), \(b_{1}\), \(c_{1}\), and \(d_{1}\). Cardiovascular aging for patients in the age range 75-89 could be described as the following differential equation:  
\[\frac{dx}{dt}=a_{2}\cdot Pr(x,t)\cdot S(x,t)+b_{2}\cdot Pr(x,t)\cdot A(x,t)+c_{2 }\cdot X(x,t)\cdot A(x,t)+d_{2}\cdot I(x,t)\cdot S(x,t), \tag{3}\]  
where \(\frac{dx}{dt}\) represents changes in premature aging over time \(t\), the first and second terms are the interactions of blood pressure with smoking and alcohol, the third term chronic heart failure with alcohol, and the fourth ischemic heart disease with smoking, respectively, with probabilities \(a_{2}\), \(b_{2}\), \(c_{2}\), and \(d_{2}\). \(a_{1}\), \(b_{1}\), \(c_{1}\), \(d_{1}\), \(a_{2}\),\(b_{2}\), \(c_{2}\), and \(d_{2}\) are interaction coefficients of the indicated markers. The derivatives of biomarkers in Equations (2) and (3) were chosen in such a way that they showed the best correlation relations. Thus, as a result, in Equations (2) and (3) of the mathematical model of premature aging of people in the age intervals 65-74 and 75-89, it can be observed that smoking and alcohol are present in all products of biomarkers, which indicates high correlation. Smoking and alcohol consumption in these age intervals can lead to postinfarction cardiosclerosis, coronary heart disease, variation in blood pressure, and changes in blood cholesterol levels. It can be concluded that people in this age range should give up bad habits in order to maintain and prevent their decline in biological age.