Plasmodium vivax is one of the most geographically widespread malaria parasites in the world, primarily found across South-East Asia, Latin America, and parts of Africa. One of the significant characteristics of the P. vivax parasite is its ability to remain dormant in the human liver as hypnozoites and subsequently reactivate after the initial infection (i.e. relapse infections). Mathematical modelling approaches have been widely applied to understand P. vivax dynamics and predict the impact of intervention outcomes. Models that capture P. vivax dynamics differ from those that capture P. falciparum dynamics, as they must account for relapses caused by the activation of hypnozoites. In this article, we provide a scoping review of mathematical models that capture P. vivax transmission dynamics published between January 1988 and May 2023. The primary objective of this work is to provide a comprehensive summary of the mathematical models and techniques used to model P. vivax dynamics. In doing so, we aim to assist researchers working on mathematical epidemiology, disease transmission, and other aspects of P. vivax malaria by highlighting best practices in currently published models and highlighting where further model development is required. We categorise P. vivax models according to whether a deterministic or agent-based approach was used. We provide an overview of the different strategies used to incorporate the parasite's biology, use of multiple scales (within-host and population-level), superinfection, immunity, and treatment interventions. In most of the published literature, the rationale for different modelling approaches was driven by the research question at hand. Some models focus on the parasites' complicated biology, while others incorporate simplified assumptions to avoid model complexity. Overall, the existing literature on mathematical models for P. vivax encompasses various aspects of the parasite's dynamics. We recommend that future research should focus on refining how key aspects of P. vivax dynamics are modelled, including spatial heterogeneity in exposure risk and heterogeneity in susceptibility to infection, the accumulation of hypnozoite variation, the interaction between P. falciparum and P. vivax, acquisition of immunity, and recovery under superinfection.

Current malaria elimination targets must withstand a colossal challenge-resistance to the current gold standard antimalarial drug, namely artemisinin derivatives. If artemisinin resistance significantly expands to Africa or India, cases and malaria-related deaths are set to increase substantially. Spatial information on the changing levels of artemisinin resistance in Southeast Asia is therefore critical for health organisations to prioritise malaria control measures, but available data on artemisinin resistance are sparse. We use a comprehensive database from the WorldWide Antimalarial Resistance Network on the prevalence of non-synonymous mutations in the Kelch 13 (K13) gene, which are known to be associated with artemisinin resistance, and a Bayesian geostatistical model to produce spatio-temporal predictions of artemisinin resistance. Our maps of estimated prevalence show an expansion of the K13 mutation across the Greater Mekong Subregion from 2000 to 2022. Moreover, the period between 2010 and 2015 demonstrated the most spatial change across the region. Our model and maps provide important insights into the spatial and temporal trends of artemisinin resistance in a way that is not possible using data alone, thereby enabling improved spatial decision support systems on an unprecedented fine-scale spatial resolution. By predicting for the first time spatio-temporal patterns and extents of artemisinin resistance at the subcontinent level, this study provides critical information for supporting malaria elimination goals in Southeast Asia.

In genetic association studies, haplotype data provide more refined information than data about separate genetic markers. However, large-scale studies that genotype hundreds to thousands of individuals may only provide results of pooled data. Methods for inferring haplotype frequencies from pooled genetic data that scale well with pool size rely on a normal approximation, which we observe to produce unreliable inference when applied to real data. We illustrate cases where the approximation fails, due to the normal covariance matrix being near-singular. As an alternative to approximate methods, in this paper we propose two exact methods to infer haplotype frequencies from pooled genetic data based on a latent multinomial model, where the pooled results are considered integer combinations of latent, unobserved haplotype counts. One of our methods, latent count sampling via Markov bases, achieves approximately linear runtime with respect to pool size. Our exact methods produce more accurate inference over existing approximate methods for synthetic data and for haplotype data from the 1000 Genomes Project. We also demonstrate how our methods can be applied to time-series of pooled genetic data, as a proof of concept of how our methods are relevant to more complex hierarchical settings, such as spatiotemporal models.

Over the past 40 years, there has been a strong focus on the development of mathematical models of angiogenesis, while developmental remodelling has received little such attention from the mathematical community. Sprouting angiogenesis can be seen as a very crude way of laying out a primitive vessel network (the raw material), while remodelling (understood as pruning of redundant vessels, diameter control, and the establishment of vessel identity and hierarchy) is the key to turning that primitive network into a functional network. This multiscale problem is of prime importance in the development of a functional vasculature. In addition, defective remodelling (either during developmental remodelling or due to a reactivation of the remodelling programme caused by an injury) is associated with a significant number of diseases. In this review, we discuss existing mathematical models of developmental remodelling and explore the important contributions that these models have made to the field of vascular development. These mathematical models are effectively used to investigate and predict vascular development and are able to reproduce experimentally observable results. Moreover, these models provide a useful means of hypothesis generation and can explain the underlying mechanisms driving the observed structural and functional network development. However, developmental vascular remodelling is still a relatively new area in mathematical biology, and many biological questions remain unanswered. In this review, we present the existing modelling paradigms and define the key challenges for the field.

BACKGROUND: Sulfadoxine-pyrimethamine (SP) is recommended in Africa in several antimalarial preventive regimens including Intermittent Preventive Treatment in pregnant women (IPTp), Intermittent Preventive Treatment in infants (IPTi) and Seasonal Malaria Chemoprevention (SMC). The effectiveness of SP-based preventive treatments are threatened in areas where Plasmodium falciparum resistance to SP is high. The prevalence of mutations in the dihydropteroate synthase gene (pfdhps) can be used to monitor SP effectiveness. IPTi-SP is recommended only in areas where the prevalence of the pfdhps540E mutation is below 50%. It has also been suggested that IPTp-SP does not have a protective effect in areas where the pfdhps581G mutation, exceeds 10%. However, pfdhps mutation prevalence data in Africa are extremely heterogenous and scattered, with data completely missing from many areas. METHODS AND FINDINGS: The WWARN SP Molecular Surveyor database was designed to summarize dihydrofolate reductase (pfdhfr) and pfdhps gene mutation prevalence data. In this paper, pfdhps mutation prevalence data was used to generate continuous spatiotemporal surface maps of the estimated prevalence of the SP resistance markers pfdhps437G, pfdhps540E, and pfdhps581G in Africa from 1990 to 2020 using a geostatistical model, with a Bayesian inference framework to estimate uncertainty. The maps of estimated prevalence show an expansion of the pfdhps437G mutations across the entire continent over the last three decades. The pfdhps540E mutation emerged from limited foci in East Africa to currently exceeding 50% estimated prevalence in most of East and South East Africa. pfdhps540E distribution is expanding at low or moderate prevalence in central Africa and a predicted focus in West Africa. Although the pfdhps581G mutation spread from one focus in East Africa in 2000, to exceeding 10% estimated prevalence in several foci in 2010, the predicted distribution of the marker did not expand in 2020, however our analysis indicated high uncertainty in areas where pfdhps581G is present. Uncertainty was higher in spatial regions where the prevalence of a marker is intermediate or where prevalence is changing over time. CONCLUSIONS: The WWARN SP Molecular Surveyor database and a set of continuous spatiotemporal surface maps were built to provide users with standardized, current information on resistance marker distribution and prevalence estimates. According to the maps, the high prevalence of pfdhps540E mutation was to date restricted to East and South East Africa, which is reassuring for continued use of IPTi and SMC in West Africa, but continuous monitoring is needed as the pfdhps540E distribution is expanding. Several foci where pfdhps581G prevalence exceeded 10% were identified. More data on the pfdhps581G distribution in these areas needs to be collected to guide IPTp-SP recommendations. Prevalence and uncertainty maps can be utilized together to strategically identify sites where increased surveillance can be most informative. This study combines a molecular marker database and predictive modelling to highlight areas of concern, which can be used to support decisions in public health, highlight knowledge gaps in certain regions, and guide future research.

Accurate knowledge of prior population exposure has critical ramifications for preparedness plans for future SARS-CoV-2 epidemic waves and vaccine prioritization strategies. Serological studies can be used to estimate levels of past exposure and thus position populations in their epidemic timeline. To circumvent biases introduced by the decay in antibody titers over time, methods for estimating population exposure should account for seroreversion, to reflect that changes in seroprevalence measures over time are the net effect of increases due to recent transmission and decreases due to antibody waning. Here, we present a new method that combines multiple datasets (serology, mortality, and virus positivity ratios) to estimate seroreversion time and infection fatality ratios (IFR) and simultaneously infer population exposure levels. The results indicate that the average time to seroreversion is around six months, IFR is 0.54% to 1.3%, and true exposure may be more than double the current seroprevalence levels reported for several regions of England.

Chronic wounds are a significant socioeconomic problem for governments worldwide. Approximately 15% of people who suffer from diabetes will experience a lower-limb ulcer at some stage of their lives, and 24% of these wounds will ultimately result in amputation of the lower limb. Hyperbaric Oxygen Therapy (HBOT) has been shown to aid the healing of chronic wounds; however, the causal reasons for the improved healing remain unclear and hence current HBOT protocols remain empirical. Here we develop a three-species mathematical model of wound healing that is used to simulate the application of hyperbaric oxygen therapy in the treatment of wounds. Based on our modelling, we predict that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds. Furthermore, treatment should continue until healing is complete, and HBOT will not stimulate healing under all circumstances, leading us to conclude that finding the right protocol for an individual patient is crucial if HBOT is to be effective. We provide constraints that depend on the model parameters for the range of HBOT protocols that will stimulate healing. More specifically, we predict that patients with a poor arterial supply of oxygen, high consumption of oxygen by the wound tissue, chronically hypoxic wounds, and/or a dysfunctional endothelial cell response to oxygen are at risk of nonresponsiveness to HBOT. The work of this paper can, in some way, highlight which patients are most likely to respond well to HBOT (for example, those with a good arterial supply), and thus has the potential to assist in improving both the success rate and hence the cost-effectiveness of this therapy.