HIV is a growing public health burden that threatens thousands of people in Kazakhstan. Countries around the world, including Kazakhstan, are facing significant problems in predicting HIV infection prevalence. It is crucial to understand the epidemiological trends of infectious diseases and to monitor the prevalence of HIV in a long-term perspective. Thus, in this study, we aimed to forecast the prevalence of HIV in Kazakhstan for 10 years from 2020 to 2030 by using mathematical modeling and time series analysis. We use statistical Autoregressive Integrated Moving Average (ARIMA) models and a nonlinear epidemic Susceptible-Infected (SI) model to forecast the HIV infection prevalence rate in Kazakhstan. We estimated the parameters of the models using open data on the prevalence of HIV infection among women and men (aged 15-49 years) in Kazakhstan provided by the Kazakhstan Bureau of National Statistics. We also predict the effect of pre-exposure prophylaxis (PrEP) control measures on the prevalence rate. The ARIMA (1,2,0) model suggests that the prevalence of HIV infection in Kazakhstan will increase from 0.29 in 2021 to 0.47 by 2030. On the other hand, the SI model suggests that this parameter will increase to 0.60 by 2030 based on the same data. Both models were statistically significant by Akaike Information Criterion corrected (AICc) score and by the goodness of fit. HIV prevention under the PrEP strategy on the SI model showed a significant effect on the reduction of the HIV prevalence rate. This study revealed that ARIMA (1,2,0) predicts a linear increasing trend, while SI forecasts a nonlinear increase with a higher prevalence of HIV. Therefore, it is recommended for healthcare providers and policymakers use this model to calculate the cost required for the regional allocation of healthcare resources. Moreover, this model can be used for planning effective healthcare treatments.