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Over the past decade, considerable progress has been made in the control, elimination, and eradication of neglected tropical diseases (NTDs). Despite these advances, most NTD programs have recently experienced important setbacks; for example, NTD interventions were some of the most frequently and severely impacted by service disruptions due to the coronavirus disease 2019 (COVID-19) pandemic. Mathematical modeling can help inform selection of interventions to meet the targets set out in the NTD road map 2021-2030, and such studies should prioritize questions that are relevant for decision-makers, especially those designing, implementing, and evaluating national and subnational programs. In September 2022, the World Health Organization hosted a stakeholder meeting to identify such priority modeling questions across a range of NTDs and to consider how modeling could inform local decision making. Here, we summarize the outputs of the meeting, highlight common themes in the questions being asked, and discuss how quantitative modeling can support programmatic decisions that may accelerate progress towards the 2030 targets.

Locally tailored interventions for neglected tropical diseases (NTDs) are becoming increasingly important for ensuring that the World Health Organization (WHO) goals for control and elimination are reached. Mathematical models, such as those developed by the NTD Modelling Consortium, are able to offer recommendations on interventions but remain constrained by the data currently available. Data collection for NTDs needs to be strengthened as better data are required to indirectly inform transmission in an area. Addressing specific data needs will improve our modelling recommendations, enabling more accurate tailoring of interventions and assessment of their progress. In this collection, we discuss the data needs for several NTDs, specifically gambiense human African trypanosomiasis, lymphatic filariasis, onchocerciasis, schistosomiasis, soil-transmitted helminths (STH), trachoma, and visceral leishmaniasis. Similarities in the data needs for these NTDs highlight the potential for integration across these diseases and where possible, a wider spectrum of diseases.

Due to the COVID-19 pandemic, many key neglected tropical disease (NTD) activities have been postponed. This hindrance comes at a time when the NTDs are progressing towards their ambitious goals for 2030. Mathematical modelling on several NTDs, namely gambiense sleeping sickness, lymphatic filariasis, onchocerciasis, schistosomiasis, soil-transmitted helminthiases (STH), trachoma, and visceral leishmaniasis, shows that the impact of this disruption will vary across the diseases. Programs face a risk of resurgence, which will be fastest in high-transmission areas. Furthermore, of the mass drug administration diseases, schistosomiasis, STH, and trachoma are likely to encounter faster resurgence. The case-finding diseases (gambiense sleeping sickness and visceral leishmaniasis) are likely to have fewer cases being detected but may face an increasing underlying rate of new infections. However, once programs are able to resume, there are ways to mitigate the impact and accelerate progress towards the 2030 goals.

In this manuscript, we present the concept of neutrosophic controlled pentagonal metric space (NCPMS), and prove some new fixed point results. Furthermore, we established many interesting outcomes for contraction maps. At last, we show the uniqueness and existence results for fractional differential and integral equations to illustrate the validity of the main outcomes. [ABSTRACT FROM AUTHOR]

Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of the world. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonald's formula for R0 and its entomological derivative, vectorial capacity, are now used to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross-Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context for mosquito blood feeding, the movement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.

In this article, we prove new common fixed-point theorems on a C ∗ -algebra-valued R -metric space. An example is given based on our obtained results. To enhance our results, a strong application based on the fractional-order initial value problem is provided. [ABSTRACT FROM AUTHOR]

Onchocerciasis, or river blindness, has historically been one of the most important causes of blindness worldwide, and a major cause of socio-economic disruption, particularly in sub-Saharan Africa. Its importance as a cause of morbidity and an impediment to economic development in some of the poorest countries in the world motivated the international community to implement several programs to control or eliminate this scourge. Initially, these involved reducing transmission of the causative agent Onchocerca volvulus through controlling the vector population. When ivermectin was found to be a very effective drug for treating onchocerciasis, the strategy shifted to mass drug administration (MDA) of endemic communities. In some countries, both vector control and ivermectin MDA have been used together. However, traditional vector control methods involve treating rivers in which the black fly vectors breed with insecticides, a process which is expensive, requires trained personnel to administer, and can be ecologically harmful. In this review, we discuss recent research into alternatives to riverine insecticide treatment, which are inexpensive, ecologically less harmful, and can be implemented by the affected communities themselves. These can dramatically reduce vector densities and, when combined with ivermectin MDA, can accelerate the time to elimination when compared to MDA alone. [ABSTRACT FROM AUTHOR]

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross-Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross-Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross-Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.

Abstract Background Large-scale intervention programmes to control or eliminate several infectious diseases are currently underway worldwide. However, a major unresolved question remains: what are reasonable stopping points for these programmes? Recent theoretical work has highlighted how the ecological complexity and heterogeneity inherent in the transmission dynamics of macroparasites can result in elimination thresholds that vary between local communities. Here, we examine the empirical evidence for this hypothesis and its implications for the global elimination of the major macroparasitic disease, lymphatic filariasis, by applying a novel Bayesian computer simulation procedure to fit a dynamic model of the transmission of this parasitic disease to field data from nine villages with different ecological and geographical characteristics. Baseline lymphatic filariasis microfilarial age-prevalence data from three geographically distinct endemic regions, across which the major vector populations implicated in parasite transmission also differed, were used to fit and calibrate the relevant vector-specific filariasis transmission models. Ensembles of parasite elimination thresholds, generated using the Bayesian fitting procedure, were then examined in order to evaluate site-specific heterogeneity in the values of these thresholds and investigate the ecological factors that may underlie such variability Results We show that parameters of density-dependent functions relating to immunity, parasite establishment, as well as parasite aggregation, varied significantly between the nine different settings, contributing to locally varying filarial elimination thresholds. Parasite elimination thresholds predicted for the settings in which the mosquito vector is anopheline were, however, found to be higher than those in which the mosquito is culicine, substantiating our previous theoretical findings. The results also indicate that the probability that the parasite will be eliminated following six rounds of Mass Drug Administration with diethylcarbamazine and albendazole decreases markedly but non-linearly as the annual biting rate and parasite reproduction number increases. Conclusions This paper shows that specific ecological conditions in a community can lead to significant local differences in population dynamics and, consequently, elimination threshold estimates for lymphatic filariasis. These findings, and the difficulty of measuring the key local parameters (infection aggregation and acquired immunity) governing differences in transmission thresholds between communities, mean that it is necessary for us to rethink the utility of the current anticipatory approaches for achieving the elimination of filariasis both locally and globally.