Until the early twentieth century, populations on many Pacific Islands had never experienced measles. As travel to the Pacific Islands by Europeans became more common, the arrival of measles and other pathogens had devastating consequences. In 1911, Rotuma in Fiji was hit by a measles epidemic, which killed 13% of the island population. Detailed records show two mortality peaks, with individuals reported as dying solely from measles in the first and from measles and diarrhoea in the second. Measles is known to disrupt immune system function. Here, we investigate whether the pattern of mortality on Rotuma in 1911 was a consequence of the immunosuppressive effects of measles. We use a compartmental model to simulate measles infection and immunosuppression. Whilst immunosuppressed, we assume that individuals are vulnerable to dysfunctional reactions triggered by either (i) a newly introduced infectious agent arriving at the same time as measles or (ii) microbes already present in the population in a pre-existing equilibrium state. We show that both forms of the immunosuppression model provide a plausible fit to the data and that the inclusion of immunosuppression in the model leads to more realistic estimates of measles epidemiological parameters than when immunosuppression is not included.

The aim of this study was to apply a comprehensive mathematical model designed to assess the current and future availability of food, as well as the resulting nutrient availability and intake, in the context of the Norwegian population. The model explores various scenarios, including self-sufficiency levels for food supply and impacts on nutrition recommendations. A food mass balance charting production, import, export, feed, seed, and consumer allocation in the Norwegian food system provided insights into the nutrients available to the population. The analysis included a comparison with two versions of the Nordic Nutrient Recommendations (NNR)1, with the latest version recommending substantial changes in food consumption compared to current dietary patterns in Norway. The nutrient analysis compared the food mass to Matvaretabellen2 and was supplemented with data from the United Nations World Population Prospects3 and the Food and Agriculture Organisation/World Health Organisation/United Nations4 report to ensure comprehensive nutrient analysis. Micronutrient gaps were observed in Iodine (94% of the target intake) and Vitamin D (46% of the target intake), while saturated-fatty acids slightly exceeded the recommended requirements (107% of the upper limit) based on the current baseline scenario. The updated NNR4 recommends changes to specific food categories, namely fruits, vegetables, nuts, and seeds. A secondary scenario testing compared against the updated NNR found that increasing the availability of the supply of these groups does not result in any new nutrient gaps, demonstrating the feasibility of addressing the issue on a national supply basis. These approach offers a mathematical-modelling based tool that can be used to provide information for a national food system. Leveraging the model’s capacity to simulate various scenarios, informed decisions to optimise self-sufficiency levels and align food supply with recommended nutritional guidelines can be made. To improve the model, higher data resolution and clearer categorisation of food groups are required which can then be linked into a more complete national food system. The mathematical model presented in this study provides a framework for understanding of food and nutrient availability in Norway. By identifying critical nutrient gaps and potential solutions, this research contributes knowledge for a healthier and sustainable food future for the nation.

In this work, a three degrees-of-freedom (3-DoF) static quadcopter unmanned aerial vehicle (UAV) test-rig of a pendulum-type configuration is custom-designed, developed, instrumented, and interfaced with a PC. The rig serves as a test bed to develop high-fidelity mathematical models as well as to investigate autopilot designs and real-time closed-loop controllers’ performances. The Simulink Desktop Real-Time software is employed for the quadcopter’s attitude signals acquisition and real-time implementation of closed-loop controllers on a target microcontroller hardware. The mathematical models for pitch, roll, and yaw axes are derived via the first principle and validated with the experimental linear system identification (SI) techniques. Subsequently, employing the multi-parameter root contour technique, the classical proportional integral derivative (PID) controllers are designed and implemented in real-time on the quadcopter UAV test rig. This served as a benchmark controller for comparing it with an integral-based linear quadratic regulator (LQR) controller. Further, to improve the transient response of the LQR controller, a novel robust integral-based LQR controller with a feedforward term (LQR-FF) is implemented, which shows much superior performance than the benchmark and basic LQR controller. This work thus will act as a precursor for a more complex 3-DoF autopilot design of an untethered quadcopter.

Introduction of African swine fever (ASF) to China in mid-2018 and the subsequent transboundary spread across Asia devastated regional swine production, affecting live pig and pork product-related markets worldwide. To explore the spatiotemporal spread of ASF in China, we reconstructed possible ASF transmission networks using nearest neighbour, exponential function, equal probability, and spatiotemporal case-distribution algorithms. From these networks, we estimated the reproduction numbers, serial intervals, and transmission distances of the outbreak. The mean serial interval between paired units was around 29 days for all algorithms, while the mean transmission distance ranged 332 –456 km. The reproduction numbers for each algorithm peaked during the first two weeks and steadily declined through the end of 2018 before hovering around the epidemic threshold value of 1 with sporadic increases during 2019. These results suggest that 1) swine husbandry practices and production systems that lend themselves to long-range transmission drove ASF spread; 2) outbreaks went undetected by the surveillance system. Efforts by China and other affected countries to control ASF within their jurisdictions may be aided by the reconstructed spatiotemporal model. Continued support for strict implementation of biosecurity standards and improvements to ASF surveillance is essential for halting transmission in China and spread across Asia.

Mosquito-borne disease is a significant public health issue and within Australia Ross River virus (RRV) is the most reported. This study combines a mechanistic model of mosquito development for two mosquito vectors; Aedes vigilax and Aedes camptorhynchus, with climate projections from three climate models for two Representative Concentration Pathways (RCPs), to examine the possible effects of climate change and sea-level rise on a temperate tidal saltmarsh habitat in Perth, Western Australia. The projections were run under no accretion and accretion scenarios using a known mosquito habitat as a case study. This improves our understanding of the possible implications of sea-level rise, accretion and climate change for mosquito control programmes for similar habitats across temperate tidal areas found in Southwest Western Australia. The output of the model indicate that the proportion of the year mosquitoes are active increases. Population abundances of the two Aedes species increase markedly. The main drivers of changes in mosquito population abundances are increases in the frequency of inundation of the tidal wetland and size of the area inundated, increased minimum water temperature, and decreased daily temperature fluctuations as water depth increases due to sea level changes, particularly under the model with no accretion. The effects on mosquito populations are more marked for RCP 8.5 when compared to RCP 4.5 but were consistent among the three climate change models. The results indicate that Ae. vigilax is likely to be the most abundant species in 2030 and 2050, but that by 2070 Aedes camptorhynchus may become the more abundant species. This increase would put considerable pressure on existing mosquito control programmes and increase the risk of mosquito-borne disease and nuisance biting to the local community, and planning to mitigate these potential impacts should commence now.

Congenital Zika is a devastating consequence of maternal Zika virus infections. Estimates of age-dependent seroprevalence profiles are central to our understanding of the force of Zika virus infections. We set out to calculate the age-dependent seroprevalence of Zika virus infections in Brazil. We analyzed serum samples stratified by age and geographic location, collected from 2016 to 2019, from about 16,000 volunteers enrolled in a Phase 3 dengue vaccine trial led by the Institute Butantan in Brazil. Our results show that Zika seroprevalence has a remarkable age-dependent and geographical distribution, with an average age of the first infection varying from region to region, ranging from 4.97 (3.03–5.41) to 7.24 (6.98–7.90) years. The calculated basic reproduction number, $ {R}_0 $, varied from region to region, ranging from 1.18 (1.04–1.41) to 2.33 (1.54–3.85). Such data are paramount to determine the optimal age to vaccinate against Zika, if and when such a vaccine becomes available.

In Beijing, the capital of China, routine measles mass vaccination has been in place for decades with high coverage; and since the 2000s, catch-up vaccination programmes have been implemented for migrant workers coming to the city. However, measles epidemics in Beijing persisted. Here, we explored the contributing factors of persistent measles transmission in Beijing using an epidemic model in conjunction with a particle filter. Model inputs included data on birth, death, migration, and vaccination. We formulated a series of hypotheses covering the impact of migrant influx, early waning of maternal immunity, and increased mixing among infants; we compared the plausibility of the hypotheses based on model fit to age-grouped, weekly measles incidence data from January 2005 to December 2014, and out-of-fit prediction during 2015–2019. Our best models showed close agreement with the data, and the out-of-fit prediction generally captured the trend of measles incidence from 2015 to 2019. We found that large influx of migrants with considerably higher susceptibility likely contributed to the persistent measles transmission in Beijing. Our findings suggest that stronger catch-up vaccination programmes for migrants may help eliminate measles transmission in Beijing.

Human monkeypox (mpox) virus is a viral zoonosis that belongs to the Orthopoxvirus genus of the Poxviridae family, which presents with similar symptoms as those seen in human smallpox patients. Mpox is an increasing concern globally, with over 80,000 cases in non-endemic countries as of December 2022. In this review, we provide a brief history and ecology of mpox, its basic virology, and the key differences in mpox viral fitness traits before and after 2022. We summarize and critique current knowledge from epidemiological mathematical models, within-host models, and between-host transmission models using the One Health approach, where we distinguish between models that focus on immunity from vaccination, geography, climatic variables, as well as animal models. We report various epidemiological parameters, such as the reproduction number, R0, in a condensed format to facilitate comparison between studies. We focus on how mathematical modelling studies have led to novel mechanistic insight into mpox transmission and pathogenesis. As mpox is predicted to lead to further infection peaks in many historically non-endemic countries, mathematical modelling studies of mpox can provide rapid actionable insights into viral dynamics to guide public health measures and mitigation strategies.

Humans harbour diverse microbial communities, and this interaction has fitness consequences for hosts and symbionts. Understanding the mechanisms that preserve host–symbiont association is an important step in studying co-evolution between humans and their mutualist microbial partners. This association is promoted by vertical transmission, which is known to be imperfect. It is unclear whether host–microbial associations can generally be maintained despite ‘leaky’ vertical transmission. Cultural practices of the host are expected to be important in bacterial transmission as they influence the host's interaction with other individuals and with the environment. There is a need to understand whether and how cultural practices affect host–microbial associations. Here, we develop a mathematical model to identify the conditions under which the mutualist can persist in a population where vertical transmission is imperfect. We show with this model that several factors compensate for imperfect vertical transmission, namely, a selective advantage to the host conferred by the mutualist, horizontal transmission of the mutualist through an environmental reservoir and transmission of a cultural practice that promotes microbial transmission. By making the host–microbe association more likely to persist in the face of leaky vertical transmission, these factors strengthen the association which in turn enables host–mutualist co-evolution.

Quantitative analysis of experimental metabolic data is frequently challenged by non-intuitive, complex patterns which emerge from regulatory networks. The complex output of metabolic regulation can be summarised by metabolic functions which comprise information about dynamics of metabolite concentrations. In a system of ordinary differential equations, metabolic functions reflect the sum of biochemical reactions which affect a metabolite concentration, and their integration over time reveals metabolite concentrations. Further, derivatives of metabolic functions provide essential information about system dynamics and elasticities. Here, invertase-driven sucrose hydrolysis was simulated in kinetic models on a cellular and subcellular level. Both Jacobian and Hessian matrices of metabolic functions were derived for quantitative analysis of kinetic regulation of sucrose metabolism. Model simulations suggest that transport of sucrose into the vacuole represents a central regulatory element in plant metabolism during cold acclimation which preserves control of metabolic functions and limits feedback-inhibition of cytosolic invertases by elevated hexose concentrations.

This paper presents a method used to rapidly assess the incursion and the establishment of community transmission of suspected SARS-CoV-2 variant of concern Delta (lineage B.1.617.2) into the UK in April and May 2021. The method described is independent of any genetically sequenced data, and so avoids the inherent lag times involved in sequencing of cases. We show that, between 1 April and 12 May 2021, there was a strong correlation between local authorities with high numbers of imported positive cases from India and high COVID-19 case rates, and that this relationship holds as we look at finer geographic detail. Further, we also show that Bolton was an outlier in the relationship, having the highest COVID-19 case rates despite relatively few importations. We use an artificial neural network trained on demographic data, to show that observed importations in Bolton were consistent with similar areas. Finally, using an SEIR transmission model, we show that imported positive cases were a contributing factor to persistent transmission in a number of local authorities, however they could not account for increased case rates observed in Bolton. As such, the outbreak of Delta variant in Bolton was likely not a result of direct importation from overseas, but rather secondary transmission from other regions within the UK.

The coronavirus disease 2019 (COVID-19) pandemic had an uneven development in different countries. In Argentina, the pandemic began in March 2020 and, during the first 3 months, the vast majority of cases were concentrated in a densely populated region that includes the city of Buenos Aires (country capital) and the Greater Buenos Aires (GBA) area that surrounds it. This work focuses on the spread of COVID-19 between June and November 2020 in GBA. Within this period of time there was no vaccine, basically only the early wild strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was present, and the official restriction and distancing measures in this region remained more or less constant. Under these particular conditions, the incidences show a sharp rise from June 2020 and begin to decrease towards the end of August until the end of November 2020. In this work we study, through mathematical modelling and available epidemiological information, the spread of COVID-19 in this region and period of time. We show that a coherent explanation of the evolution of incidences can be obtained assuming that only a minority fraction of the population got involved in the spread process, so that the incidences decreased as this group of people was becoming immune. The observed evolution of the incidences could then be a consequence at the population level of lasting immunity conferred by SARS-CoV-2.

Self-instigated isolation is heavily relied on to curb severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission. Accounting for uncertainty in the latent and prepatent periods, as well as the proportion of infections that remain asymptomatic, the limits of this intervention at different phases of infection resurgence are estimated. We show that by October 2020, SARS-CoV-2 transmission rates in England had already begun exceeding levels that could be interrupted using this intervention alone, lending support to the second national lockdown on 5th November 2020.

Estimating the case fatality ratio (CFR) for COVID-19 is an important aspect of public health. However, calculating CFR accurately is problematic early in a novel disease outbreak, due to uncertainties regarding the time course of disease and difficulties in diagnosis and reporting of cases. In this work, we present a simple method for calculating the CFR using only public case and death data over time by exploiting the correspondence between the time distributions of cases and deaths. The time-shifted distribution (TSD) analysis generates two parameters of interest: the delay time between reporting of cases and deaths and the CFR. These parameters converge reliably over time once the exponential growth phase has finished. Analysis is performed for early COVID-19 outbreaks in many countries, and we discuss corrections to CFR values using excess-death and seroprevalence data to estimate the infection fatality ratio (IFR). While CFR values range from 0.2% to 20% in different countries, estimates for IFR are mostly around 0.5–0.8% for countries that experienced moderate outbreaks and 1–3% for severe outbreaks. The simplicity and transparency of TSD analysis enhance its usefulness in characterizing a new disease as well as the state of the health and reporting systems.

During the coronavirus disease 2019 (COVID-19) pandemic, many countries opted for strict public health measures, including closing schools. After some time, they have started relaxing some of those restrictions. To avoid overwhelming health systems, predictions for the number of new COVID-19 cases need to be considered when choosing a school reopening strategy. Using a computer simulation based on a stochastic compartmental model that includes a heterogeneous and dynamic network, we analyse different strategies to reopen schools in the São Paulo Metropolitan Area, including one similar to the official reopening plan. Our model allows us to describe different types of relations between people, each type with a different infectiousness. Based on our simulations and model assumptions, our results indicate that reopening schools with all students at once has a big impact on the number of new COVID-19 cases, which could cause a collapse of the health system. On the other hand, our results also show that a controlled school reopening could possibly avoid the collapse of the health system, depending on how people follow sanitary measures. We estimate that postponing the schools' return date for after a vaccine becomes available may save tens of thousands of lives just in the São Paulo Metropolitan Area compared to a controlled reopening considering a worst-case scenario. We also discuss our model constraints and the uncertainty of its parameters.

In this paper, we present a method to estimate the risk of reopening of schools illustrated with the case of the State of São Paulo, Brazil. The model showed that, although no death of children would result from the reopening of the schools in the three cities analysed, the risk of asymptomatic and symptomatic cases and secondary cases among teachers, school staff and relatives of the children is not negligible. Although the epidemic hit different regions with different intensities, our model shows that, for regions where the incidence profile is similar to the cities analysed, the risk of reopening of schools is still too high. This in spite of the fact that incidences in these cities were declining in the period of the time considered. Therefore, although we cannot extend the result to the entire country, the overall conclusion is valid for regions with a declining incidence and it is even more valid for regions where incidence is increasing. We assumed a very conservative level of infection transmissibility of children of just 10% as that of adults. In spite of the very low level of transmissibility is assumed, the number of secondary cases caused by infected children among teachers, school staff and relatives varied from 2 to 85. It is, therefore, too soon to have any degree of confidence that reopening of schools before the advent of a vaccine is the right decision to take. The purpose of our model and simulations is to provide a method to estimate the risk of school reopening, although we are sure it could be applied as a guide to public health strategies.

This study aimed to identify an appropriate simple mathematical model to fit the number of coronavirus disease 2019 (COVID-19) cases at the national level for the early portion of the pandemic, before significant public health interventions could be enacted. The total number of cases for the COVID-19 epidemic over time in 28 countries was analysed and fit to several simple rate models. The resulting model parameters were used to extrapolate projections for more recent data. While the Gompertz growth model (mean R2 = 0.998) best fit the current data, uncertainties in the eventual case limit introduced significant model errors. However, the quadratic rate model (mean R2 = 0.992) fit the current data best for 25 (89%) countries as determined by R2 values of the remaining models. Projection to the future using the simple quadratic model accurately forecast the number of future total number of cases 50% of the time up to 10 days in advance. Extrapolation to the future with the simple exponential model significantly overpredicted the total number of future cases. These results demonstrate that accurate future predictions of the case load in a given country can be made using this very simple model.