Gaining insights into human viral diseases through mathematics

Models of Respiratory Infections: Virus-Induced Asthma Exacerbations and Beyond

Respiratory infections are one of the main health problems worldwide. They are a challenging field of study due to an intricate relationship between the pathogenicity of microbes and the host's defenses. To better understand mechanisms of respiratory infections, different models have been developed. A model is the reproduction of a disease in a system that mimics human pathophysiology. For this reason, the best models should closely resemble real-life conditions. Thus, the human model is the best. However, human models of respiratory infections have some disadvantages that limit their role. Therefore, other models, including animal, in vitro, and mathematical ones, have been developed. We will discuss advantages and limitations of available models and focus on models of viral infections as triggers of asthma exacerbations, viral infections being one of the most frequent causes of exacerbating disease. Future studies should focus on the interrelation of various models.

Public health interventions for epidemics: implications for multiple infection waves

BACKGROUND

Epidemics with multiple infection waves have been documented for some human diseases, most notably during past influenza pandemics. While pathogen evolution, co-infection, and behavioural changes have been proposed as possible mechanisms for the occurrence of subsequent outbreaks, the effect of public health interventions remains undetermined.

METHODS

We develop mean-field and stochastic epidemiological models for disease transmission, and perform simulations to show how control measures, such as drug treatment and isolation of ill individuals, can influence the epidemic profile and generate sequences of infection waves with different characteristics.

RESULTS

We demonstrate the impact of parameters representing the effectiveness and adverse consequences of intervention measures, such as treatment and emergence of drug resistance, on the spread of a pathogen in the population. If pathogen resistant strains evolve under drug pressure, multiple outbreaks are possible with variability in their characteristics, magnitude, and timing. In this context, the level of drug use and isolation capacity play an important role in the occurrence of subsequent outbreaks. Our simulations for influenza infection as a case study indicate that the intensive use of these interventions during the early stages of the epidemic could delay the spread of disease, but it may also result in later infection waves with possibly larger magnitudes.

CONCLUSIONS

The findings highlight the importance of intervention parameters in the process of public health decision-making, and in evaluating control measures when facing substantial uncertainty regarding the epidemiological characteristics of an emerging infectious pathogen. Critical factors that influence population health including evolutionary responses of the pathogen under the pressure of different intervention measures during an epidemic should be considered for the design of effective strategies that address short-term targets compatible with long-term disease outcomes.

Mathematical modeling and the epidemiological research process

The authors of this paper advocate for the expanded use of mathematical models in epidemiology and provide an overview of the principles of mathematical modeling. Mathematical models can be used throughout the epidemiological research process. Initially they may help to refine study questions by visually expressing complex systems, directing literature searches, and identifying sensitive variables. In the study design phase, models can be used to test sampling strategies, to estimate sample size and power, and to predict outcomes for studies impractical due to time or ethical considerations. Once data are collected, models can assist in the interpretation of results, the exploration of causal pathways, and the combined analysis of data from multiple sources. Finally, models are commonly used in the process of applying research findings to public health practice by estimating population risk, predicting the effects of interventions, and contributing to the evaluation of ongoing programs. Mathematical modeling has the potential to make significant contributions to the field of epidemiology by enhancing the research process, serving as a tool for communicating findings to policymakers, and fostering interdisciplinary collaboration.