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Identifiability of a mathematical model plays a crucial role in the parameterization of the model. In this study, we established the structural identifiability of a susceptible-exposed-infected-recovered (SEIR) model given different combinations of input data and investigated practical identifiability with respect to different observable data, data frequency, and noise distributions. The practical identifiability was explored by both Monte Carlo simulations and a correlation matrix approach. Our results showed that practical identifiability benefits from higher data frequency and data from the peak of an outbreak. The incidence data gave the best practical identifiability results compared to prevalence and cumulative data. In addition, we compared and distinguished the practical identifiability by Monte Carlo simulations and a correlation matrix approach, providing insights into when to use which method for other applications. 

Death is a common outcome of infection, but most disease models do not track hosts after death. Instead, these hosts disappear into a void. This assumption lacks critical realism, because dead hosts can alter host–pathogen dynamics. Here, we develop a theoretical framework of carbon‐based models combining disease and ecosystem perspectives to investigate the consequences of feedbacks between living and dead hosts on disease dynamics and carbon cycling. Because autotrophs (i.e. plants and phytoplankton) are critical regulators of carbon cycling, we developed general model structures and parameter combinations to broadly reflect disease of autotrophic hosts across ecosystems. Analytical model solutions highlight the importance of disease–ecosystem coupling. For example, decomposition rates of dead hosts mediate pathogen spread, and carbon flux between live and dead biomass pools are sensitive to pathogen effects on host growth and death rates. Variation in dynamics arising from biologically realistic parameter combinations largely fell along a single gradient from slow to fast carbon turnover rates, and models predicted higher disease impacts in fast turnover systems (e.g. lakes and oceans) than slow turnover systems (e.g. boreal forests). Our results demonstrate that a unified framework, including the effects of pathogens on carbon cycling, provides novel hypotheses and insights at the nexus of disease and ecosystem ecology.