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.

Since their first detection in 2010, Plasmodium falciparum malaria parasites lacking the P. falciparum histidine-rich protein 2 gene (pfhrp2) have been observed in 40 of 47 surveyed countries, as documented by the World Health Organization. These genetic deletions reduce detection by the most widely used rapid diagnostic tests, prompting three countries to switch to alternative diagnostics. However, manufacturing of alternative rapid diagnostic tests has not been scaled up and there are no World Health Organization-prequalified combination tests that use P. falciparum Plasmodium lactate dehydrogenase. The continuing spread of pfhrp2 and/or pfhrp3 (pfhrp2/3) deletions threatens malaria control, creating an emerging public health crisis. Here we use mathematical modeling informed by current pfhrp2/3 deletion prevalence and a literature review to assess the global risk of pfhrp2 /3 deletions. We identify ten priority countries for surveillance and predict that the primary spread in Africa will move southward from the Horn of Africa through East Africa within 20 years. Despite variation in modeled timelines due to uncertainty in model parameters, four countries yet to switch rapid diagnostic tests are consistently classified as high risk under a range of model assumptions. This updated model offers refined predictions to guide pfhrp2/3 policy and prioritize future surveillance efforts and innovation.

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.

Access to medical treatment for fever is essential to prevent morbidity and mortality in individuals and to prevent transmission of communicable febrile illness in communities. Quantification of the rates at which treatment is accessed is critical for health system planning and a prerequisite for disease burden estimates. In this study, national data on the proportion of children under five years old with fever who were taken for medical treatment were collected from all available countries in Africa, Latin America, and Asia (n = 91). We used generalised additive mixed models to estimate 30-year trends in the treatment-seeking rates across the majority of countries in these regions (n = 151). Our results show that the proportions of febrile children brought for medical treatment increased steadily over the last 30 years, with the greatest increases occurring in areas where rates had originally been lowest, which includes Latin America and Caribbean, North Africa and the Middle East (51 and 50% increase, respectively), and Sub-Saharan Africa (23% increase). Overall, the aggregated and population-weighted estimate of children with fever taken for treatment at any type of facility rose from 61% (59–64 95% CI) in 1990 to 71% (69–72 95% CI) in 2020. The overall population-weighted average for fraction of treatment in the public sector was largely unchanged during the study period: 49% (42–58 95% CI) sought care at public facilities in 1990 and 47% (44–52 95% CI) in 2020. Overall, the findings indicate that improvements in access to care have been made where they were most needed, but that despite rapid initial gains, progress can plateau without substantial investment. In 2020 there remained significant gaps in care utilisation that must be factored in when developing control strategies and deriving disease burden estimates.

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.

No studies have yet examined high-resolution shifts in the spatial patterns of human movement in Australia throughout 2020 and 2021, a period coincident with the repeated enactment and removal of varied governmental restrictions aimed at reducing community transmission of SARS-CoV-2. We compared overlapping timeseries of COVID-19 pandemic-related restrictions, epidemiological data on cases and vaccination rates, and high-resolution human movement data to characterize population-level responses to the pandemic in Australian cities. We found that restrictions on human movement and/or mandatory business closures reduced the average population-level weekly movement volumes in cities, as measured by aggregated travel time, by almost half. Of the movements that continued to occur, long movements reduced more dramatically than short movements, likely indicating that people stayed closer to home. We also found that the repeated lockdowns did not reduce their impact on human movement, but the effect of the restrictions on human movement waned as the duration of restrictions increased. Lastly, we found that after restrictions ceased, the subsequent surge in SARS-CoV-2 transmission coincided with a substantial, non-mandated drop in human movement volume. These findings have implications for public health policy makers when faced with anticipating responses to restrictions during future emergency situations.