<p>This study investigates the integration of statistical models ARIMA, vector autoregression (VAR), and Gaussian process (GP) with machine learning techniques such as long short-term memory (LSTM) networks to predict COVID-19 infection trends. Statistical models effectively capture linear patterns and temporal dependencies, while advanced machine learning models like LSTM excel in modelling nonlinear relationships and long-term dependencies. By combining these methodologies, hybrid models leverage the strengths of both approaches to provide robust and accurate forecasts, overcoming the limitations of standalone models. This paper also conducts a comparative analysis of three hybrid models: ARIMA-LSTM, VAR-LSTM, and GP-LSTM, using real-world epidemiological data. Each hybrid model integrates the linear capabilities of statistical methods with the nonlinear learning process of LSTM networks to predict infection trends. Five evaluation metrics are employed to assess performance comprehensively: Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and the coefficient of determination (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>). These metrics ensure a rigorous evaluation of predictive accuracy and model reliability. The results highlight the effectiveness of combining statistical and machine learning models for enhanced forecasting accuracy. Among the hybrid models, GP-LSTM exhibited superior performance, underscoring its potential for supporting data-driven public health strategies and decision-making during epidemics.</p>