Mathematical Modeling and Computation of Emerging Infectious Diseases

Abstract

The study of complex dynamics in epidemiology and biology increasingly employs mathematical modeling for explanation, analysis, and prediction. As the global threat of emerging and re-emerging infectious diseases persists, model-based approaches continue to play a vital role in understanding the transmission dynamics and designing public health interventions. When developing mathematical models for infectious disease, deterministic models, which fully specify the parameter values and the initial conditions without randomness, have been widely used. This study develops deterministic mathematical models to investigate the transmission dynamics and evaluate control strategies for two emerging infectious diseases: Coronavirus Disease (COVID-19) and Severe Fever with Thrombocytopenia Syndrome (SFTS). For COVID-19, a compartmental model with age structure was designed to reflect the final phase of the COVID-19 pandemic in Korea, incorporating key factors such as the vaccination status of the population, the testing status of the contagious population, and the severity of confirmed cases. Scenario analysis was conducted to assess the effects of two main interventions: the mandatory quarantine period for confirmed cases and indoor mask-wearing, which were maintained until the end of the COVID-19 pandemic in Korea. In addition, the interpretation of control interventions from the economic perspective was provided by estimating the total cost due to changes in interventions. In contrast to COVID-19, which spreads primarily through human-to-human contact, SFTS is one of the vector-borne diseases transmitted via the bite of infected ticks. To represent this main transmission route of SFTS, first, the stage-structured compartment model that accounts for the life cycle of ticks was introduced, with climate-dependent parameters governing the transition between life stages. Based on this ecological model, the model was expanded to the entire transmission dynamics of SFTS with tick-human interaction. Simulations based on scenarios were conducted to examine the impact of climate change and control strategies on tick population and SFTS transmission. Moreover, a cost-benefit analysis was conducted to evaluate the economic implications of control measures on tick population and associated with tick-borne diseases and climate change. By applying tailored mathematical modeling approaches to diseases with different transmission routes, this study provides a quantitative framework for analyzing the biological, epidemiological, and environmental factors that shape infectious disease dynamics. The scenario analysis and cost analysis provide appropriate intervention strategies not only to control diseases but also to reduce the economic burden in an era of ecological and epidemiological uncertainty.