This article reviews modern applications of mathematical descriptions of biofilm formation. The focus is on theoretically obtained results which have implications for areas including the medical sector, food industry and wastewater treatment. Examples are given as to how models have contributed to the overall knowledge on biofilms and how they are used to predict biofilm behaviour. We conclude that the use of mathematical models of biofilms has demonstrated over the years the ability to significantly contribute to the vast field of biofilm research. Among other things, they have been used to test various hypotheses on the nature of interspecies interactions, viability of biofilm treatment methods or forces behind observed biofilm pattern formations. Mathematical models can also play a key role in future biofilm research. Many models nowadays are analysed through computer simulations and continue to improve along with computational capabilities. We predict that models will keep on providing answers to important challenges involving biofilm formation. However, further strengthening of the ties between various disciplines is necessary to fully use the tools of collective knowledge in tackling the biofilm phenomenon.

Campylobacter jejuni is a bacterial pathogen recognised as a major cause of foodborne illness worldwide. While Campylobacter jejuni generally does not grow outside its host, it can survive outside of the host long enough to pose a health concern. This review presents an up-to-date description and evaluation of biological, mathematical, and statistical approaches used to understand the behaviour of this foodborne pathogen and suggests future avenues which can be explored. Specifically, the incorporation of mathematical modelling may aid the understanding of C. jejuni biofilm formation both outside and inside the host. Predictive studies may be improved by the introduction of more standardised protocols for assessments of disinfection methods and by assessment of novel physical disinfection strategies as well as assessment of the efficiency of plant extracts on C. jejuni eradication. A full description of the metabolic pathways of C. jejuni, which is needed for the successful application of metabolic models, is yet to be achieved. Finally, a shift from animal models (except for those that are a source of human campylobacteriosis) to human-specific data may be made possible due to recent technological advancements, and this may lead to more accurate predictions of human infections.

The COVID-19 pandemic has led to far-reaching disruptions to health systems, including preventative and curative services for malaria. The aim of this study was to estimate the magnitude of disruptions in malaria case management in sub-Saharan Africa and their impact on malaria burden during the COVID-19 pandemic. We used survey data collected by the World Health Organization, in which individual country stakeholders reported on the extent of disruptions to malaria diagnosis and treatment. The relative disruption values were then applied to estimates of antimalarial treatment rates and used as inputs to an established spatiotemporal Bayesian geostatistical framework to generate annual malaria burden estimates with case management disruptions. This enabled an estimation of the additional malaria burden attributable to pandemic-related impacts on treatment rates in 2020 and 2021. Our analysis found that disruptions in access to antimalarial treatment in sub-Saharan Africa likely resulted in approximately 5.9 (4.4–7.2 95% CI) million more malaria cases and 76 (20–132) thousand additional deaths in the 2020–2021 period within the study region, equivalent to approximately 1.2% (0.3–2.1 95% CI) greater clinical incidence of malaria and 8.1% (2.1–14.1 95% CI) greater malaria mortality than expected in the absence of the disruptions to malaria case management. The available evidence suggests that access to antimalarials was disrupted to a significant degree and should be considered an area of focus to avoid further escalations in malaria morbidity and mortality. The results from this analysis were used to estimate cases and deaths in the World Malaria Report 2022 during the pandemic years.