Modelling and analysis of the effects of malnutrition in the spread of cholera

Smart waterborne disease control for a scalable population using biodynamic model in IoT network

We propose a biodynamic model for managing waterborne diseases over an Internet of Things (IoT) network, leveraging the scalability of LoRa IoT technology to accommodate a growing human population. The model, based on fractional order derivatives (FOD), enables smart prediction and control of pathogens that cause waterborne diseases using IoT infrastructure. The human-pathogen-based biodynamic FOD model utilises epidemic parameters (SVIRT: susceptibility, vaccination, infection, recovery, and treatment) transmitted over the IoT network to predict pathogenic contamination in water reservoirs and dumpsites in Iji-Nike, Enugu, the study community in Nigeria. These pathogens contribute to person-to-person, water-to-person, and dumpsite-to-person transmission of disease vectors. Five control measures are proposed: potable water supply, treatment, vaccination, adequate sanitation, and health education campaigns. A stable disease-free equilibrium point is found when the effective reproduction number of the pathogens, R0eff<1 and unstable if R0eff>1. While other studies showed a 98.2% reduction in infections when using IoT alone, this paper demonstrates that combining the SVIRT epidemic control parameters (such as potable water supply and health education campaign) with IoT achieves a 99.89% reduction in infected human populations and a 99.56% reduction in pathogen populations in water reservoirs. Furthermore, integrating treatment with sanitation results in a 99.97% reduction in infected populations. Finally, combining these five control strategies nearly eliminates infection and pathogen populations, demonstrating the effectiveness of multifaceted approaches in public health and environmental management. This study provides a blueprint for governments to plan sustainable smart cities for a growing population, ensuring potable water free from pathogenic contamination,in line with the United Nations Sustainable Development Goals #6 (Clean Water and Sanitation) and #11 (Sustainable Cities and Communities).

Experience of caregivers on the continuum of care and prevention of malnutrition among children with cholera in Ethiopia: a phenomenology study

INTRODUCTION

Malnutrition is a public health problem in low- and middle-income countries among children. Although illnesses such as diarrhea are common immediate drivers of childhood malnutrition, their consequences could be averted through optimal sick child feeding and care to ensure the continuum of care. This study aimed to explore the lived experiences of mothers/caregivers on continuum of care to prevent malnutrition among children with cholera in Ethiopia.

METHODS

A phenomenology study design was applied to explore experiences of mothers/caregivers in the Bale and Guji zones of the Oromia region, southeast Ethiopia, from November to December 2022 using an unstructured interview guide. The saturation of ideas was used to stop the in-depth interview. Translated data were cleaned and imported into ATLAS.ti7 software for analysis. Using an open coding system, the data were coded into a meaningful context. Deeper immersion into data with repeated reading, creating themes, subthemes, and family/category were carried out. In coding and categorization, multiple coders were involved. The finding was presented using well-spoken verbatim/quotes as illustrations and in narratives.

RESULTS

In this qualitative study, ten participants were taken to explore their lived experience on the continuum of care for children with acute malnutrition and cholera. The study found that poverty, expensive cost of living, and poor utilization of diversified food were challenges. Moreover, health facilities did not provide any services to mothers whose child was admitted for malnutrition treatment. Children five years and above were excluded from both therapeutic food and screening for malnutrition program. Interruptions of supplies, low attention given to child feeding, inadequate knowledge, and lack of time to prepare diversified food were the main findings.

CONCLUSION

Poverty, poor feeding habits, supplies interruption and non-inclusion of malnourished children five and above in screening for malnutrition and in the therapeutic feeding program is missed opportunities that lead to decreased early detection and treatment of malnutrition among children with cholera. Moreover, mothers/caregivers did not receive any service from health facilities when their child was admitted for treatment of malnutrition. This situation forces them to stop treatment before their child recovers from malnutrition, which has a negative impact on the continuum of care and prevention of malnutrition. Therefore, we strongly recommend strengthening emergency nutrition within the country's health system and revising the food and nutrition policy to incorporate emergency nutrition, with a particular focus on children under the age of fifteen. Additionally, it is important that the study's recommendations underscore the significance of a multi-sectoral approach that involves collaboration among the health sector, government agencies, and non-governmental organizations. Moreover, adaptive agricultural products be made easily accessible to the community which is crucial in effective preventing and reducing malnutrition in children in the study and similar settings.

Association between air raids and reported incidence of cholera in Yemen, 2016-19: an ecological modelling study

BACKGROUND

Yemen continues to endure cholera outbreaks during ongoing conflict and destructive environmental events. Air raids have been used throughout the conflict to target military and civilian infrastructure. We aimed to assess the association between air raids and cholera incidence while taking into account geographical, environmental, economic, and demographic factors that drive outbreaks.

METHODS

In this ecological modelling study, we used data from Sept 12, 2016, to Dec 29, 2019, for the number of air raids, vegetation coverage, surface water, precipitation, temperature, economic variables, and cholera case and population data to model the association between conflict and the weekly incidence of cholera (per 100 000 people) in Yemen. Data were transformed into weekly intervals and governorates were categorised according to air raid severity (the number of raids in the previous 3 months). We used a negative binomial generalised additive model that accounted for geographical location and environmental, temporal, economic, and demographic variables to estimate incidence rate ratios for the association between air raid severity and cases of cholera.

FINDINGS

During the study period, 2 107 912 cases of cholera were reported in Yemen, and a minimum of 11 366 air raids were recorded. After controlling for relevant factors, compared with no air raids, all other levels of air raid severity were significantly associated with cholera incidence. The largest effect was noted in governorates with severe air raid levels (ie, ≥76 during the previous 3 months), which had an incidence rate ratio of 2·06 (95% CI 1·59-2·69; p<0·0001) for cholera compared with governorates with no air raids in the previous 3 months. Economic factors were also significantly associated with increased cholera incidence.

INTERPRETATION

Air raids were significantly associated with the burden of cholera in Yemen, even after controlling for other relevant factors. Quantification of this relationship further shows that the cholera outbreak is largely a result of human action rather than a natural occurrence, and demonstrates the conflict's devastating effects on health. Our findings highlight the need for ceasefire and peacebuilding efforts, as well as infrastructure and economic restoration, to reduce Yemen's cholera burden.

FUNDING

None.

TRANSLATION

For the Arabic translation of the abstract see Supplementary Materials section.

A mathematical model for the impact of disinfectants on the control of bacterial diseases

Here, we investigate a mathematical model to assess the impact of disinfectants in controlling diseases that spread in the population via direct contacts with the infected persons and also due to bacteria present in the environment. We find that the disease-free and endemic equilibria of the system are related via a transcritical bifurcation whose direction is forward. Our numerical results show that controlling the transmissions of disease through direct contacts and bacteria present in the environment can help in reducing the disease prevalence. Moreover, fostering the recovery rate and the death rate of bacteria play significant roles in disease eradication. Our numerical observations convey that reducing the bacterial density at the source discharged by the infected population through the use of chemicals has prominent effect in disease control. Overall, our findings manifest that the disinfectants of high quality can completely control the bacterial density and the disease outbreak.

Dynamic mapping of cholera outbreak during the Yemeni Civil War, 2016-2019

Widespread destruction from the Yemeni Civil War (2014-present) triggered the world's largest cholera outbreak. We compiled a comprehensive health dataset and created dynamic maps to demonstrate spatiotemporal changes in cholera infections and war conflicts. We aligned and merged daily, weekly, and monthly epidemiological bulletins of confirmed cholera infections and daily conflict events and fatality records to create a dataset of weekly time series for Yemen at the governorate level (subnational regions administered by governors) from 4 January 2016 through 29 December 2019. We demonstrated the use of dynamic mapping for tracing the onset and spread of infection and manmade factors that amplify the outbreak. We report curated data and visualization techniques to further uncover associations between infectious disease outbreaks and risk factors and to better coordinate humanitarian aid and relief efforts during complex emergencies.

NICOV : a model to analyse impact of nutritional status and immunity on COVID-19

A few months back there was no medication and vaccine for COVID-19. Yet, most of the infected people got recovered. A very small portion of the infected people could not recover. A lion’s share of the fatal cases were the patients suffering from some kind of chronic critical diseases. Due to that, their nutritional status and immunity were not normal. In this study, we have proposed a model called NICOV (Nutritional status, Immunity and COVID) that establishes the relationship among nutritional status, immunity, and COVID-19. This model formulates the relations considering all possible states of nutritional status and immunity of the body. We have numerically simulated the model for four different sets of values and found that susceptible, infected, and recovered cases of COVID-19 are significantly related to different states of nutritional status and immunity. It is also evident from numerical simulation that the effect of nutritional status and immunity varies with variation of other parameters associated with the formulation of the model. This model can help the concerned in decision making for mitigation of the losses that arise due to COVID-19-like situations.

Stability Analysis and Optimal Control of a Fractional Cholera Epidemic Model

In this paper, a fractional model for the transmission dynamics of cholera was developed. In invariant regions of the model, solutions were generated. Disease-free and endemic equilibrium points were obtained. The basic reproduction number was evaluated, and the sensitivity analysis was performed. Under the support of Pontryagin’s maximum principle, the fractional order optimal control was obtained. Furthermore, an optimal strategy was discussed, which minimized the total number of infected individuals and the costs associated with control. Treatment, vaccination, and awareness programs were regarded as three means to reduce the number of infected. Finally, numerical simulations and cost-effectiveness analysis were presented to show the result that the best strategy was the combination of treatment and awareness programs.

A SIQRB delayed model for cholera and optimal control treatment

We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a L1 type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite - Haiti, from 1 November 2010 to 1 May 2011, than the non-delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication.

Signatures of Cholera Outbreak during the Yemeni Civil War, 2016-2019

The Global Task Force on Cholera Control (GTFCC) created a strategy for early outbreak detection, hotspot identification, and resource mobilization coordination in response to the Yemeni cholera epidemic. This strategy requires a systematic approach for defining and classifying outbreak signatures, or the profile of an epidemic curve and its features. We used publicly available data to quantify outbreak features of the ongoing cholera epidemic in Yemen and clustered governorates using an adaptive time series methodology. We characterized outbreak signatures and identified clusters using a weekly time series of cholera rates in 20 Yemeni governorates and nationally from 4 September 2016 through 29 December 2019 as reported by the World Health Organization (WHO). We quantified critical points and periods using Kolmogorov–Zurbenko adaptive filter methodology. We assigned governorates into six clusters sharing similar outbreak signatures, according to similarities in critical points, critical periods, and the magnitude of peak rates. We identified four national outbreak waves beginning on 12 September 2016, 6 March 2017, 28 May 2018, and 28 January 2019. Among six identified clusters, we classified a core regional hotspot in Sana’a, Sana’a City, and Al-Hudaydah—the expected origin of the national outbreak. The five additional clusters differed in Wave 2 and Wave 3 peak frequency, timing, magnitude, and geographic location. As of 29 December 2019, no governorates had returned to pre-Wave 1 levels. The detected similarity in outbreak signatures suggests potentially shared environmental and human-made drivers of infection; the heterogeneity in outbreak signatures implies the potential traveling waves outwards from the core regional hotspot that could be governed by factors that deserve further investigation.

Modeling the Effectiveness of TV and Social Media Advertisements on the Dynamics of Water-Borne Diseases

Cholera is a serious threat to the health of human-kind all over the world and its control is a problem of great concern. In this context, a nonlinear mathematical model to control the prevalence of cholera disease is proposed and analyzed by incorporating TV and social media advertisements as a dynamic variable. It is considered that TV and social media ads propagate the knowledge among the people regarding the severe effects of cholera disease on human health along with its precautionary measures. It is also assumed that the mode of transmission of cholera disease among susceptible individuals is due to consumption of contaminated drinking water containing Vibrio cholerae. Moreover, the propagation of knowledge through TV and social media ads makes the people aware to adopt precautionary measures and also the aware people make some effectual efforts to washout the bacteria from the aquatic environment. Model analysis reveals that increase in the washout rate of bacteria due to aware individuals causes the stability switch. It is found that TV and social media ads have the potential to reduce the number of infectives in the region and thus control the cholera epidemic. Numerical simulation is performed for a particular set of parameter values to support the analytical findings.

Risk structured model of cholera infections in Cameroon

Since 1991, Cameroon, a cholera endemic African country, has been experiencing large cholera outbreaks and cholera related deaths. In this paper, we use a "fitted" demographic equation (disease-free equation) to capture the total population of Cameroon, and then use a fitted low-high risk structured cholera differential equation model to study reported cholera cases in Cameroon from 1987 to 2004. For simplicity, our model has no spatial structure. The basic reproduction number of our fitted cholera model, R₀, is bigger than 1 and our model predicted cholera endemicity in Cameroon. In addition, the fitted risk structured model predicted a decreasing trend from 1987 to 1994 and an increasing trend from 1995 to 2004 in the pre-intervention reported number of cholera cases in Cameroon from 1987 to 2004. Using the fitted risk structured cholera model, we study the impact of vaccination, treatment and improved sanitation on the number of cholera infections in Cameroon from 2004 to 2022. The dual strategies of either vaccination and treatment or vaccination and improved sanitation or the combined strategy of vaccination, treatment and improved sanitation reduce the basic reproduction number of Cameroon from 1.1803 to 0.9982, 1.1803 to 0.9987 and 1.1803 to 0.9952, respectively, and the number of cholera cases by 99.6735%, 98.7498% and 99.7280%, respectively. Thus, each of these three strategies is capable of eliminating cholera in Cameroon with the combined strategy having the lowest value for the effective reproduction number, R_E, and the highest percentage decrease in the number of cholera cases. Finally, using sensitivity analysis, we study the impact of our model parameters on the demographic threshold, basic reproduction number, effective reproduction number and on the total number of our model's predicted cholera cases.

Modelling cholera transmission dynamics in the presence of limited resources

Objectives

We study the transmission dynamics of cholera in the presence of limited resources, a common feature of the developing world. The model is used to gain insight into the impact of available resources of the health care system on the spread and control of the disease. A deterministic model that includes a nonlinear recovery rate is formulated and rigorously analyzed. Limited treatment is described by inclusion of a special treatment function. Center manifold theory is used to show that the model exhibits the phenomenon of backward bifurcation. Matlab has been used to carry out numerical simulations to support theoretical findings.

Results

The model analysis shows that the disease free steady state is locally stable when the threshold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{0} < 1$$\end{document}R0<1. It is also shown that the model has multiple equilibria and the model exhibits the phenomenon of backward bifurcation whose implications to cholera infection are discussed. The results are useful for the public health planning in resource allocation for the control of cholera transmission.

Analysis of a waterborne disease model with socioeconomic classes

Waterborne diseases such as cholera continue to pose serious public health problems in the world today. Transmission parameters can vary greatly with socioeconomic class (SEC) and the availability of clean water. We formulate a multi-patch waterborne disease model such that each patch represents a particular SEC with its own water source, allowing individuals to move between SECs. For a 2-SEC model, we investigate the conditions under which each SEC is responsible for driving a cholera outbreak. We determine the effect of SECs on disease transmission dynamics by comparing the basic reproduction number of the 2-SEC model to that of a homogeneous model that does not take SECs into account. We conclude by extending several results of the 2-SEC model to an n-SEC model.

SPATIO-TEMPORAL PATTERNS IN A CHOLERA TRANSMISSION MODEL

Cholera has been a public health threat for centuries. Unlike the biological characteristics, relatively less effort has been paid to comprehend the spatial dynamics of this disease. Therefore, in this paper, we have proposed a cholera epidemic model for variable population size and studied the spatial patterns in two-dimensional space. First, we have performed the equilibrium and local stability analysis of steady states obtained for temporal system. Afterwards, the local and global stability behavior of the endemic steady state in a spatially extended setting has been investigated. The numerical simulations have been done to investigate the spatial patterns. They show that dynamics of the cholera epidemic varies with time and space.

MODELING CHOLERA DISEASE WITH EDUCATION AND CHLORINATION

Cholera, characterized by severe diarrhea and rapid dehydration, is a water-borne infectious disease caused by the bacterium Vibrio cholerae. Haiti offers the most recent example of the tragedy that can befall a country and its people when cholera strikes. While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate and analyze a mathematical model that includes two essential and affordable control measures: water chlorination and education. We calculate the basic reproduction number and determine the global stability of the disease-free equilibrium for the model without chlorination. We use Latin Hypercube Sampling to demonstrate that the model is most sensitive to education. We also derive the minimal effective chlorination period required to control the disease for both fixed and variable chlorination. Numerical simulations suggest that education is more effective than chlorination in decreasing bacteria and the number of cholera cases.

Dynamics of Vibrio with virulence genes detected in Pacific harbor seals (Phoca vitulina richardii) off California: implications for marine mammal health

Given their coastal site fidelity and opportunistic foraging behavior, harbor seals (Phoca vitulina) may serve as sentinels for coastal ecosystem health. Seals using urbanized coastal habitat can acquire enteric bacteria, including Vibrio that may affect their health. To understand Vibrio dynamics in seals, demographic and environmental factors were tested for predicting potentially virulent Vibrio in free-ranging and stranded Pacific harbor seals (Phoca vitulina richardii) off California. Vibrio prevalence did not vary with season and was greater in free-ranging seals (29 %, n = 319) compared with stranded seals (17 %, n = 189). Of the factors tested, location, turbidity, and/or salinity best predicted Vibrio prevalence in free-ranging seals. The relationship of environmental factors with Vibrio prevalence differed by location and may be related to oceanographic or terrestrial contributions to water quality. Vibrio parahaemolyticus, Vibrio alginolyticus, and Vibrio cholerae were observed in seals, with V. cholerae found almost exclusively in stranded pups and yearlings. Additionally, virulence genes (trh and tdh) were detected in V. parahaemolyticus isolates. Vibrio cholerae isolates lacked targeted virulence genes, but were hemolytic. Three out of four stranded pups with V. parahaemolyticus (trh+ and/or tdh+) died in rehabilitation, but the role of Vibrio in causing mortality is unclear, and Vibrio expression of virulence genes should be investigated. Considering that humans share the environment and food resources with seals, potentially virulent Vibrio observed in seals also may be of concern to human health.

Dynamics analysis of a multi-strain cholera model with an imperfect vaccine

A new two-strain model, for assessing the impact of basic control measures, treatment and dose-structured mass vaccination on cholera transmission dynamics in a population, is designed. The model has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. The model has a unique, and locally-asymptotically stable, endemic equilibrium when the threshold quantity exceeds unity and another condition holds. Numerical simulations of the model show that, with the expected 50% minimum efficacy of the first vaccine dose, vaccinating 55% of the susceptible population with the first vaccine dose will be sufficient to effectively control the spread of cholera in the community. Such effective control can also be achieved if 50% of the first vaccine dose recipients take the second dose. It is shown that a control strategy that emphasizes the use of antibiotic treatment is more effective than one that emphasizes the use of basic (non-pharmaceutical) anti-cholera control measures only. Numerical simulations show that, while the universal strategy (involving all three control measures) gives the best outcome in minimizing cholera burden in the community, the combined basic anti-cholera control measures and treatment strategy also has very effective community-wide impact.

Distinguishing between indirect and direct modes of transmission using epidemiological time series

Pathogen transmission can involve direct and/or indirect pathways. Using theoretical models, in this study we ask, "do directly and indirectly transmitted pathogens yield different population-level epidemiological dynamics?" and "can the transmission pathway be inferred from population-level epidemiological data?" Our approach involves comparing the continuous-time dynamics of a class of compartmental epidemiological models with direct versus environmentally mediated indirect transmission pathways. Combing analytical theory and numerical simulations we show that models with direct and indirect transmission can produce quantitatively similar time series when the pathogen cannot reproduce in the environment, particularly when the environmental pathogen dynamics are fast. We apply these results to a previous study on chronic wasting disease and show that identifying the transmission pathway is more difficult than previously acknowledged. Our analysis and simulations also yield conditions under which numerical differences can potentially identify the transmission route in oscillating endemic systems and systems where the environmental pathogen dynamics are not fast. This work begins to identify how differences in the transmission pathway can result in quantitatively different epidemiological dynamics and how those differences can be used to identify the transmission pathway from population level time series.

Mathematical modeling of liver enzyme elevation in HIV mono-infection

HIV-infected individuals are increasingly becoming susceptible to liver disease and, hence, liver-related mortality is on a rise. The presence of CD4+ in the liver and the presence of C-X-C chemokine receptor type 4 (CXCR4) on human hepatocytes provide a conducive environment for HIV invasion. In this study, a mathematical model is used to analyse the dynamics of HIV in the liver with the aim of investigating the existence of liver enzyme elevation in HIV mono-infected individuals. In the presence of HIV-specific cytotoxic T-lymphocytes, the model depicts a unique endemic equilibrium with a transcritical bifurcation when the basic reproductive number is unity. Results of the study show that the level of liver enzyme alanine aminotransferase (ALT) increases with increase in the rate of hepatocytes production. Numerical simulations reveal significant elevation of alanine aminotransferase with increase in viral load. The findings presuppose that while liver damage in HIV infection has mostly been associated with HIV/HBV coinfection and use of antiretroviral therapy (ART), it is possible to have liver damage solely with HIV infection.

Modeling huanglongbing transmission within a citrus tree

The citrus disease huanglongbing (HLB), associated with an uncultured bacterial pathogen, is threatening the citrus industry worldwide. A mathematical model of the transmission of HLB between its psyllid vector and citrus host has been developed to characterize the dynamics of the vector and disease development, focusing on the spread of the pathogen from flush to flush (a newly developing cluster of very young leaves on the expanding terminal end of a shoot) within a tree. This approach differs from that of prior models for vector-transmitted plant diseases where the entire plant is the unit of analysis. Dynamics of vector and host populations are simulated realistically as the flush population approaches complete infection. Model analysis indicates that vector activity is essential for initial infection but is not necessary for continued infection because infection can occur from flush to flush through internal movement in the tree. Flush production, within-tree spread, and latent period are the most important parameters influencing HLB development. The model shows that the effect of spraying of psyllids depends on time of initial spraying, frequency, and efficacy of the insecticides. Similarly, effects of removal of symptomatic flush depend on the frequency of removal and the time of initiation of this practice since the start of the epidemic. Within-tree resistance to spread, possibly affected by inherent or induced resistance, is a major factor affecting epidemic development, supporting the notion that alternate routes of transmission besides that by the vector can be important for epidemic development.