A general deterministic model of ordinary differential equations for a broad variety of different diseases

The COVID-19 pandemic underscored the pivotal role of mathematical models in comprehending pandemic dynamics and making accurate predictions under diverse interventions. Various mathematical models, particularly deterministic ones, have proven valuable for analyzing the impact of political, social, and medical measures during ongoing pandemics. In this study, we aim to formulate and characterize a comprehensive model applicable to different infectious diseases. Reviewing numerous disease-specific models reveals a common foundation in the Kermack–McKendrick model (SIR model). While there are more general versions incorporating population dynamics, vector populations, and vaccination, none encompass all attributes simultaneously. To address this gap, we propose a comprehensive general model capable of accommodating different transmission modes, pandemic control measures, and diverse pathogens. Unlike disease-specific models, having such a pre-established model with foundational mathematical properties analyzed eliminates the need to reevaluate these characteristics for each new disease-specific model. This article presents our comprehensive general model, supported by mathematical analysis and numerical simulations, offering a versatile tool for understanding the dynamics of emerging infectious diseases and guiding intervention strategies. The applicability of the model is demonstrated through simulations.