Mathematical Models Take Center Stage in the Fight Against Infectious Disease

Infectious diseases remain one of the most formidable burdens on public health worldwide, and their transmission is governed by a tangled interplay between pathogens, hosts, environment, human behavior, healthcare capacity, and public health interventions. The emergence and resurgence of diseases such as COVID-19, dengue, and influenza, alongside coinfections, pathogen evolution, and disruption of healthcare systems, have exposed the limits of purely empirical approaches to epidemic management. A new collection of research published in Frontiers in Applied Mathematics and Statistics argues that mathematical modeling offers a formal, rigorous alternative: a way to represent the processes involved in disease spread, identify the key drivers of transmission, evaluate interventions before they are deployed, and explore epidemic dynamics under deep uncertainty.

The collection, assembled as a Research Topic titled Advances in Mathematical Modelling for Infectious Disease Control and Prevention, brings together eight studies that span an extraordinary range of biological scales and methodological traditions. Edited by Fahad Al Basir of Asansol Girls’ College in India and Khalid Hattaf of Hassan II University of Casablanca in Morocco, the Research Topic pursues three interrelated goals: understanding the mechanisms underlying infectious diseases, predicting their dynamics, and ensuring effective control and prevention. According to the editors, recent advances in the field have produced models that account for biological delays, coinfection, disease progression, vector-host interaction, and the constraints of healthcare systems, while machine learning, artificial intelligence, and time series analysis now offer powerful tools for analyzing large-scale epidemiological datasets.

At the mechanistic end of the spectrum, Elaiw and colleagues investigated the within-host infection dynamics of a simultaneous HIV and HBV infection using a nonlinear delayed system model. The inclusion of delay parameters, which capture the lagged nature of viral dynamics, makes the system considerably more realistic than instantaneous formulations. By analyzing the stability and long-term behavior of the modeled system, the study demonstrates how delay differential equations can reveal whether a coinfection settles into a persistent state or is driven toward clearance, a question of direct clinical relevance for patients carrying both viruses.

Mathematics can also connect infection dynamics to their long-term consequences, as shown by Amanso and coauthors, who built a model for human papillomavirus infections and cervical cancer prevention. Their framework incorporates disease progression and interventions including vaccination, awareness campaigns, screening, and treatment. Using sensitivity analysis and an optimal control approach, they explored the impact of intervention measures, identifying strategies that minimize both infection and cancer incidence at acceptable cost. The work is a striking example of how mathematical models can bridge the gap between a viral infection today and a malignancy decades later, giving policymakers a quantitative basis for investing in prevention.

The scope of the Research Topic extends beyond human medicine into agriculture. Collins and colleagues extended infectious disease modeling to plant pathology with a study of African cassava mosaic virus and East African cassava mosaic Cameroon virus, two pathogens that devastate a staple crop across much of the developing world. Their model considers disease dynamics and control in the presence of both infected plants and the whiteflies that transmit the viruses, making the study directly relevant to the agricultural and food industries. Because cassava feeds hundreds of millions of people, plant-virus modeling of this kind carries implications for food security that are every bit as serious as those of human epidemic models.

A second cluster of studies turns to the interaction between disease spread and the resilience of healthcare systems. Shaale and coauthors examined the effects of healthcare breakdown on nosocomial infections, constructing a model that explores how reduced healthcare capacity can contribute to rising hospital-acquired infections through weakened infection control measures and the persistence of pathogens in the hospital environment. The importance of this work is especially pronounced because infection control cannot be viewed separately from the healthcare environment itself. Models that explicitly incorporate the capacity of the healthcare system, the editors note, can yield additional insight into infection control problems that capacity-blind models miss entirely, a lesson underlined by the strains placed on hospitals during recent global emergencies.

While mechanistic models focus on the process of transmission, forecasting models aim to predict future epidemic behavior, and the Research Topic features several computational contributions in this vein. Demongeot and colleagues studied epidemic peak forecasting for COVID-19 and dengue by relying on the index of dispersion of new cases, a fairly simple statistical measure. Their research underscores the capabilities of parsimonious approaches while pointing to the importance of surveillance and reporting systems, since even the simplest forecasting statistic is only as good as the case data feeding it.

More sophisticated signal-processing and machine-learning techniques appear in the work of Feng and coauthors, who developed an approach to long-term forecasting of influenza epidemics using spectral filtering and a frequency-aligned loss function. By aligning the training objective with the frequency content of epidemic time series, the authors showed the effectiveness of applying tools from signal processing to traditional epidemiological forecasting, capturing seasonal patterns that standard loss functions can obscure. In a related contribution, Wang and colleagues compared time-series foundation models, namely TimesFM and Moirai, with ARIMA and LSTM networks in their ability to forecast hand, foot and mouth disease. The comparison drew on data from Korea, Singapore, and Chongqing and involved various forecasting horizons, and its findings show that the effectiveness of forecasting depends on the model, the horizon, and the specifics of the data, with no single architecture dominating across all settings.

The final contribution addresses a problem that is sometimes neglected in mathematical modeling: making a model sustainable for public health practice. Thakur and coauthors reflected on lessons learned from the development of the California Communicable Diseases Assessment Tool, known as CalCAT, a public health dashboard built on mathematical modeling. CalCAT illustrates that the usefulness of an infectious disease model goes far beyond its mathematical structure. Proper implementation, the authors argue, involves a reliable data pipeline, transparency of uncertainty estimates, validation against observed outcomes, and sustained interaction with users. If a model is not sustainable and not capable of being used by working epidemiologists, its usefulness is questionable, however elegant its equations may be.

Taken together, the eight studies reveal two complementary trends shaping the future of the field. The first is increasing biological and mathematical complexity, with models incorporating coinfections, time delays, disease progression, vector-host dynamics, and healthcare system limitations. The second is computational convergence, as machine learning, foundation models, time series analysis, and decision-support platforms are folded into the modeling workflow. The editors suggest that future infectious disease modeling will benefit most from the combined use of both traditions: mechanistic models contribute biological plausibility and interpretability, while data-driven models help discover patterns in large datasets. Yet uncertainty remains essential, because epidemiological measurements are subject to incomplete surveillance, reporting delays, changes in behavior and policy, and pathogen adaptation. The central theme of the collection is clear: mathematical models perform at their best when theory and data are combined in the context of real-world public health issues, and continued progress will depend on state-of-the-art techniques, high-quality data, realistic assumptions, proper validation, interdisciplinary collaboration, and clear communication with the practitioners who rely on these models for preparedness and prevention.

Subject of Research: Infectious Disease Modelling

Article Title: Editorial: Advances in mathematical modelling for infectious disease control and prevention

Article References: Al Basir, F., & Hattaf, K. (2026). Editorial: Advances in mathematical modelling for infectious disease control and prevention. Frontiers in Applied Mathematics and Statistics, 12, Article 2016937. https://doi.org/10.3389/fams.2026.2016937

Image Credits: AI Generated

DOI: 10.3389/fams.2026.2016937

Keywords: mathematical modelling, infectious disease, epidemiology, machine learning, public health, forecasting, Editorial, Advances, mathematical, modelling, infectious, disease