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Abstract: Measles, a member of the Paramyxoviridae family and the Morbillivirus genus, is an infectious disease caused by the measles virus that is extremely contagious and can be prevented through vaccination. When a person with the measles coughs or sneezes, the virus is disseminated by respiratory droplets. Normally, the appearance of measles symptoms takes 10-14 d following viral exposure. Conjunctivitis, a high temperature, a cough, a runny nose, and a distinctive rash are some of the symptoms. Despite the measles vaccination being available, it is still widespread worldwide. To eradicate measles, the Reproduction Number (i.e. R0<1) must remain less than unity. This study examines a SEIVR compartmental model in the caputo sense using a double dose of vaccine to simulate the measles outbreak. The reproduction number R0 and model properties are both thoroughly examined. Both the local and global stabilities of the proposed model are determined for R0 less and greater than 1. To achieve the model's global stability, the Lyapunov function is used while the existence and uniqueness of the proposed model are demonstrated In addition to the calculated and fitted biological parameters, the forward sensitivity indices for R0 are also obtained. Simulations of the proposed fractional order (FO) caputo model are performed in order to analyse their graphical representations and the significance of FO derivatives to illustrate how our theoretical findings have an impact. The graphical results show that the measles outbreak is reduced by increasing vaccine dosage rates.

Abstract: The administration of the Measles, Mumps, and Rubella (MMR) vaccination has had a substantial impact on controlling the spread of measles on a global scale. Nevertheless, the COVID-19 pandemic caused major disruptions to normal immunization schedules, causing the omission or delay of routine immunizations. Expanding on previous research that simulated measles outbreaks using a detailed agent-based model, this study integrates epidemiological forecasts with spatial econometrics analysis. Our objective is to quantify the household-level direct and indirect health and economic impact of measles outbreaks caused by reduction in MMR vaccine uptake. A network-based SEIR (susceptible-exposed-infected-recovered) model is used to simulate the transmission of measles over a synthetic social contact network of Virginia, under various scenarios. Household-level costs of measles outbreak, encompassing MMR vaccine expenses, treatment costs, and productivity losses, are estimated from the simulation results. A Generalized Spatial Autoregressive (GSAR) model is used to estimate the spatial 'spillover effect' on neighboring counties. Our findings indicate that reduced MMR vaccination rates are associated with increased measles cases and related economic costs, which are intensified by disease transmissibility and moderated by home quarantine. The GSAR model, with spatial lag coefficients, shows significant spatial interdependencies. A small decrease in vaccination rate in an urban region like Richmond, Virginia, has significant economic and epidemiological spillover effect, while similar reductions in rural regions like Highland County, Virginia, have a negligible impact. A decline in MMR vaccination rate has ramifications for both disease incidence and the economy, presenting diverse consequences influenced by regional disparities. Policymakers should acknowledge the interconnectedness of health and economic outcomes across regions. This research underscores the necessity of implementing broad, region-wide policy measures in response to fluctuations in vaccination rates, prioritizing overarching strategies over localized interventions.

Abstract: This study uses actual data from Pakistan to investigate an established mathematical framework that describes the dynamics and epidemiology of measles transmission. Sanitation and immunization are taken as mitigating strategies in the model. The primary model's six components are Susceptible, Recovered, Infected, Exposed, Hospitalized, and Vaccinated that can be addressed semi-analytically using the homotopy analysis approach. To show the influence of various model parameter categories including the frequency of hospitalized persons with measles visit due to complications, rate of vaccinating susceptible class and recruitment rate into susceptible class, graphical illustrations are provided. The outcomes show that this approach is the most practical, easy to use, and efficient. A satisfactory match is obtained by comparing the findings with the numerical simulation (MATLAB). This technique will be extended to tackle epidemic models especially, SIR, SEIR, SVIR, SVEIR,SLVEIR based on malaria, chikungunya, tuberculosis, HIV, hepatitis A virus, typhoid, Ebola, Cholera etc.

Abstract: Measles is a severe infectious respiratory disease that predominantly affects children and is largely preventable by vaccination. Despite the availability of a vaccine, measles continues to pose a significant threat to global health management. The disease is the primary cause of illness and death in children under five years of age. The majority of measles-related fatalities occur in countries with inadequate health infrastructure and low per capita income. In this study, a fractional order mathematical model is constructed for the population of individuals infected with measles, divided into three compartments: the number of susceptible individuals (S), the number of infected individuals (I), the number of vaccinated and recovered individuals (V). The Caputo derivative definition was employed as the fractional derivative. The stability analysis of the fractional model for measles was conducted, and numerical solutions were obtained through the utilisation of the Euler method. Consequently, the dynamics of the number of individuals with measles disease in a population were created and interpreted.

Abstract: Models of measles transmission can be used to identify areas of high risk to tailor immunization strategies. Estimates of spatial connectivity can be derived from data such as mobile phone records, but it is not clear how this maps to the movement of children who are more likely to be infected. Using travel surveys across 2 districts in Zambia and national mobile phone data, we compared estimates of out-of-district travel for the population captured in the mobile phone data and child-specific travel from travel surveys. We then evaluated the impact of unadjusted and adjusted connectivity measures on simulated measles virus introduction events across Zambia. The number of trips made by children from the travel survey was 3 to 5 times lower than the general population estimates from mobile phone data. This decreased the percentage of districts with measles virus introduction events from 78% when using unadjusted data to 51% to 64% following adjustment. Failure to account for age-specific heterogeneities in travel estimated from mobile phone data resulted in overestimating subnational areas at high risk of introduction events, which could divert mitigation efforts to districts that are at lower risk.

Abstract: The worldwide measles crisis has escalated into a significant public health issue due to its lethal nature,
generating widespread anxiety. Our study presents a dynamic mathematical model constructed using comprehen
sive mortality data from the World Health Organization and actual data on measles outbreak propagation. By
utilizing the Routh-Hurwitz criteria and formulating Lyapunov functions, we demonstrated both local and global stability for scenarios with and without the presence of the disease. Furthermore, we conducted a sensitivity analysis on the model’s parameters to assess their impact on the basic reproduction number, R0. Our theoretical results
were substantiated through numerical simulations performed with MATLAB.

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Abstract: In this study, we studied the spread of measles using the SEIR (Susceptible-Exposed-Infectious-Recovered) epidemic model, which we treated as a Markov chain. In epidemiology, a stationary distribution means that the disease will continue spreading until a vaccine is found. Our study presents a Markovian SEIR model to analyze the long-term behavior of measles transmission. Unlike deterministic models, our approach incorporates stochastic dynamics by computing the stationary distribution, offering insights into disease persistence. We employ the state reduction method to simplify complex computations and develop a Mathematica-based algorithm to efficiently determine steady-state probabilities. The findings provide a probabilistic understanding of measles spread, helping to assess vaccination strategies and long-term control measures.

Abstract: Measles is a highly contagious and sometimes fatal viral disease that continues to pose a significant threat across the globe, particularly in areas with low vaccination coverage. Despite the availability of effective vaccination, measles outbreaks continue, highlighting the urgent need for stronger preventive measures. This study proposes a mathematical model that classifies the population into five categories. This is based on the epidemiological status of individuals in the population: susceptible, vaccinated, exposed, infected, and recovered individuals. The study investigates how various control strategies, such as vaccination, public health education, and considering the impact of waning immunity, can help prevent the spread of measles. To estimate the parameters of our model, we fit the model to the observed data obtained from the Nigeria Centre for Disease Control using cumulative weekly reported measles case data from Nigeria, covering January to December 2024. We calculate the effective reproduction number (RE) to see how the disease spreads under different settings, and we utilize sensitivity analysis to discover which factors have the greatest impact. The findings indicate that measles transmission rate and vaccine effectiveness are the most critical drivers of disease spread. Public health education, represented by a parameter in the model, also plays an important role in reducing dangerous behaviors and transmission. Numerical simulations show that increased vaccination coverage and public awareness campaigns greatly lower the incidence of illnesses. The findings indicate that in order to effectively reduce measles, we need a multifaceted approach that combines broad vaccination, efforts to improve vaccine quality, and robust public health education campaigns. These ideas can guide governments and health organizations in formulating effective policies to avoid future outbreaks and safeguard public health.

Abstract: Measles remains a major global public health challenge despite available vaccines. To evaluate the combined impact of routine immunization and supplementary vaccination campaigns, we developed a compartmental mathematical model that incorporates declining immunity and breakthrough infections. We derived the control reproduction number using the next-generation matrix method, analyzed stability and bifurcation properties of the equilibria, and conducted sensitivity analysis to determine key drivers of transmission. The model was parameterized from the literature and calibrated to 2024 Nigerian measles case data using Markov Chain Monte Carlo sampling. The model revealed that the disease-free equilibrium is globally stable when the control reproduction number is less than one, but a backward bifurcation indicates that reducing the reproduction number below unity may not suffice for elimination. Sensitivity analysis identified the transmission rate among vaccinated individuals, breakthrough infections, and waning immunity as dominant drivers of transmission. Simulations demonstrated that while routine vaccination delays and reduces outbreak peaks, it does not interrupt transmission alone; annual campaigns outperform biennial strategies, preventing 40% more cases; and combined vaccination reduces the reproduction number below unity while preventing 65-80% of infections versus no vaccination. Critically, temporary disruptions in routine coverage significantly increase outbreak risk, and maintaining vaccine efficacy above 90% alongside hospitalization of at least 50% of infectious individuals is essential for containment. These results underscore that high-coverage routine vaccination must be integrated with periodic high-intensity campaigns and robust clinical care to close immunity gaps, mitigate waning protection, and accelerate measles elimination.

Abstract: The time-series Susceptible-Infectious-Recovered (TSIR) model has been a standard tool for studying the non-linear dynamics of acute, immunizing infectious diseases. The standard assumption of the TSIR model, that vaccination is equivalent to a reduction in the recruitment of susceptible individuals, or the birth rate, can lead to a bias in the estimate of the reporting fraction and of the total incidence. We show that this bias increases with the level of vaccination due to a double counting of individuals who are infected prior to the age of vaccination. We present a simple correction for this bias by discounting the observed number of cases by the product of the number that occur prior to the average age of vaccination and the vaccination coverage during the initial susceptible reconstruction step of the TSIR model fitting. We generate a time series of measles cases using an age-structured SIR transmission model with vaccination after birth (at 9 months of age) and illustrate the bias with the standard TSIR fitting method. We then illustrate that our proposed correction eliminates the bias in the estimated reporting fraction and total incidence. We note further that this bias does not impact the estimates of the seasonality of transmission.

Abstract: Quantifying population mobility is crucial in developing accurate models of infectious disease dynamics. Increasingly, multiple data sources are available to describe individual and population mobility in a single location; however, there are no methods to systematically integrate these data. Combining information from these data sets may be valuable and help mitigate inherent biases in each data set due to sampling, censoring, and recall. We examined four commonly used data sources (mobile phone records, travel survey, Demographic and Health Survey, and Facebook location information) to quantify subnational travel patterns in Zambia. First, we explored summary metrics of mobility from each data set. Estimates of the probability of a trip and location of travel varied across data sets, with some data quantifying twice the frequency of travel as others. Then, we developed a departure-diffusion model that is able to produce a single estimate of travel by combining these data sets. When multi-data set models included mobile phone records, this data source dominated estimates given the broader spatial coverage. We then used a metapopulation model to simulate a measles outbreak to identify how these different data sets and models would impact estimates of the spatial spread of a highly infectious disease. We found that using travel survey data to parameterize mobility resulted in the introduction of cases in 98% of districts compared to less than 50% when mobile phone data or Facebook data were used. This study highlights the need for methods that facilitate integrating multiple data sets to improve validity of mobility estimates and resultant infectious disease transmission dynamics.

Abstract: A novel mathematical model which explores the transmission dynamics of infectious diseases integrating nonlinear incidence and quarantine measures is presented in this study. Five different compartments: susceptible, latent, infectious, quarantined and recovered individuals presents total population. Saturation effects in disease transmission are modeled through a nonlinear infection rate while quarantine and recovery processes are explicitly incorporated. Parameters are estimated using a genetic algorithm based on cumulative monthly case data for measles in Indonesia. The basic reproduction number is derived to assess the potential for outbreak persistence. Stability analysis of the equilibrium states is conducted, and sensitivity analysis identifies key parameters influencing disease spread. Furthermore, the model is extended using Atangana-Baleanu Caputo (ABC) fractional derivative to explore memory-dependent effects in disease dynamics. Numerical simulations illustrate how fractional-order values impact infection trajectories. The findings emphasize the importance of timely isolation and recovery in controlling outbreaks and suggest that fractional-order modeling can enhance understanding of long-term epidemic behavior.

Abstract: Measles, an exceedingly contagious but vaccine-preventable disease, is a global peril causing an overwhelming count of deaths, especially of younger children taking place in lousy economic countries. In countries with poor socio-economic ambience, the health infrastructure is very fragile. Measles infection in adults having no vaccination against Measles or the adults whose immunity against Measles is waned is in substantial risk of being infected, and the infection might be life-threatening. The transmission chain of Measles in adults causes disruption in economic stability of low economy countries via disruption in labor supply chain. To systematically measure the impact of Measles transmission in economy of a geographical region (specially of low economy) and the effect of optimal vaccination level in mitigating the transmission, a novel seven-compartment ODE deterministic SVMIRPE model is proposed in the present study. The qualitative behaviors of the model are studied, and the basic reproduction number of the model is computed. The steady states of the system are investigated, and we perform stability analysis of the system around the steady states. To ensure the maximum effectiveness of Measles vaccination with minimum cost, optimal control strategies are determined suggesting utilization of the vaccine on global basis. Moreover, we upgrade our proposed model to an impulsive differential equation model to find optimal vaccination time intervals and to determine the threshold count of infected persons for mass vaccination. The numerical results confirm the analytical predictions and illustrate that the model can predict Measles dynamics under different economic and vaccination scenarios. This epidemiological study provides practical guidance for health policy makers in making socio-economic policies of cost-efficient mass vaccination and in planning long-term control of Measles.

Abstract: Outbreaks of vaccine-preventable diseases frequently occur in low and middle-income countries (LMICs), requiring outbreak response immunisation (ORI) programmes for containment. To inform future investment decisions, this study aimed to estimate the cases, deaths, disability-adjusted life years (DALYs) and societal economic costs averted by past ORI programmes. Outbreaks of measles, Ebola, yellow fever, cholera and meningococcal meningitis in LMICs between 2000 and 2023 were considered. 210 outbreaks (51 measles, 40 cholera, 88 yellow fever, 24 meningitis, 7 Ebola) across 49 LMICs were identified with sufficient data for analysis. Data were sourced from publicly available outbreak reports and literature. Agent-based models were calibrated for each disease such that after controlling for baseline vaccine coverage, response time, vaccination rate, environmental variables or endemic revalence of the disease, observed outbreaks were within the distribution of simulated outbreaks. A status-quo and no ORI scenario were compared for each outbreak. Across 210 outbreaks, ORI programmes are estimated to have averted 5.81M (95% uncertainty interval 5.75M-5.87M) cases (4.01M measles, 283K cholera, 1.50M yellow fever, 21.3K meningitis, 820 Ebola), 327K (317K-338K) deaths (20.0K measles, 5215 cholera, 300K yellow fever, 1599 meningitis, 381 Ebola), 14.6M (14.1M-15.1M) DALYs (1.27M measles, 220K cholera, 13.0M yellow fever, 113K meningitis, 16.6K Ebola) and US$31.7B (29.0B-34.9B) (US$710M measles, US$156M cholera, US$30.7B yellow fever, US$97.6M meningitis, US$6.72M Ebola) in economic costs. Often, the more rapidly the ORI was initiated the greater impact.

Abstract: The 7-1-7 targets are gaining traction as measurable targets for assessing a country's readiness to detect and respond to outbreaks of infectious diseases. The targets are outbreak detection within 7 days of emergence, notification to health authorities within 1 day, and key early response actions commenced within another 7 days. For outbreaks of measles, cholera, yellow fever, and meningococcal meningitis, we estimated the impact of initiating outbreak response immunisation (ORI) within 15 days of outbreak emergence, relative to the mean ORI response time for each disease in low- and middle-income countries (LMICs) since 2000. Initiating ORI within 15 days of outbreak emergence aligns with the 7-1-7 targets and supports outbreak containment. Using agent-based models for four diseases, a status quo and series of 'Faster response' scenarios were compared for simulated outbreaks of each disease, with a 15-day ORI response time as the minimum. The Starsim modelling framework was used to build the models to provide a single common software and analysis architecture for all models while having the flexibility to account for very different modes of transmission across the diseases being modelled. The models were calibrated to epidemiological and programmatic response data for 51 measles, 40 cholera, 24 meningococcal meningitis, and 88 yellow fever outbreaks in LMICs. In a synthetic model population, a 15-day ORI response could avert: 80% of cases from cholera outbreaks relative to a historical response time of 105 days, 35% of cases from meningococcal meningitis outbreaks relative to a historical response time of 75 days, 0-35% of cases from yellow fever outbreaks relative to a historical response time of 105 days (depending on routine vaccine coverage and environmental suitability), and 0-55% of cases from measles outbreaks relative to a historical response time of 120 days (depending on routine vaccine coverage). Improvements made to ORI response time could reduce disease burden and decrease the risk of large outbreaks of vaccine-preventable diseases in LMICs. Efforts to improve ORI timeliness should be prioritised to higher risk settings, and it was clear that even a slow vaccination response was beneficial relative to no response at all.

Abstract: The time-to-recovery or time-to-death for various infectious diseases can vary significantly among individuals, influenced by several factors such as demographic differences, immune strength, medical history, age, pre-existing conditions, and infection severity. To capture these variations, time-since-infection dependent recovery and death rates offer a detailed description of the epidemic. However, obtaining individual-level data to estimate these rates is challenging, while aggregate epidemiological data (such as the number of new infections, number of active cases, number of new recoveries, and number of new deaths) are more readily available. In this article, a new methodology is proposed to estimate time-since-infection dependent recovery and death rates using easily available data sources, accommodating irregular data collection timings reflective of real-world reporting practices. The Nadaraya-Watson estimator is utilized to derive the number of new infections. This model improves the accuracy of epidemic progression descriptions and provides clear insights into recovery and death distributions. The proposed methodology is validated using COVID-19 data and its general applicability is demonstrated by applying it to some other diseases like measles and typhoid.

Abstract: Many countries schedule a second dose of measles-containing vaccine (MCV2) for children in their second year of life. The correlation between recipients of the first dose of measles-containing vaccine (MCV1) and MCV2 is poorly understood but is important for estimating population levels of measles immunity and for meeting elimination targets. Using data from 19 surveys from Demographic and Health Surveys (DHS) we computed the percentage of MCV1 recipients with subsequent MCV2 and of MCV2 recipients with previous MCV1. All countries included in our study recommended MCV1 in the first year of life and MCV2 in the second year of life. For 2 surveys we computed the variation of those percentages over the country's geographical regions. We computed adjusted odds ratios for the association of this percentage with age, sex, residency, mother's education, wealth and birth order. For most of the surveys, over 50% of MCV1 recipients received MCV2, but there was more than 30% MCV1 to MCV2 dropout in more than half of the surveys. The percentage of MCV1 recipients with MCV2 was statistically significantly higher if they received MCV1 below age 12 months and the percentage increased with increasing education status of the mother and higher income levels. A small number of MCV2 recipients were not found to have received MCV1, despite marked on record as having received MCV2 implies having previously received MCV1 (by definition of the survey data collection methodology). Our analyses have highlighted important shortfalls by age, country, mother's education and income status in the proportion of MCV1 recipients who subsequently receive MCV2. Targeting those differentials is essential for achieving the goals of measles elimination.

Abstract: Poverty alleviation is a major global development goal. Vaccines have the potential to provide financial risk protection (FRP) by preventing illnesses and associated healthcare costs. We estimate the lifetime FRP benefits generated by major vaccines among individuals vaccinated between 2000 and 2030 in low- and middle-income countries (LMICs). We developed a microsimulation model to quantify the number of cases of catastrophic health expenditure (CHE) averted by a range of vaccines in 52 Gavi-eligible countries, stratified by wealth quintile. Vaccines protecting against five pathogens were considered, i.e., hepatitis B (routine and birth dose vaccine), Haemophilus influenzae type B, rotavirus, measles (routine and supplementary campaign vaccine), and Streptococcus pneumoniae. Model inputs were obtained from secondary data sources, including infection reduction rates under various immunization coverage scenarios, out-of-pocket health expenditures, transportation costs, wage losses, and healthcare utilization associated with disease treatment and consumption expenditures. CHE cases were defined as exceeding 10% of annual consumption, with sensitivity analyses conducted using thresholds of 25% and 40%, as well as impoverishing health expenditures were estimated. All vaccines, singly and collectively, showed a large impact on FRP and could avert ~200 million CHE cases across 52 Gavi-eligible countries from 2000 to 2030. Importantly, about half of all CHE cases were prevented among the poorest quintiles. When evaluated at a 10% threshold for CHE, the first dose of measles vaccine stood out in averting around 1,400 CHE cases per 10,000 vaccinated individuals in the poorest quintile, that is a total of 44 million CHE cases averted. A key limitation is the assumption of uniform disease risks in the absence of vaccination across quintiles, which may underestimate benefits for poorer groups. Vaccines can provide substantial FRP benefits, particularly among the most disadvantaged populations. Sustained investments to ensure vulnerable populations receive vaccinations in

Abstract: In many settings, ongoing measles transmission is maintained due to pockets of un- or under-vaccinated individuals even if the critical vaccination threshold is reached nationwide. Therefore, assessing the underlying gaps in measles susceptibility within a population is essential for vaccination programs and measles control efforts. Recently, there have been increased efforts to use geospatial and small area methods to estimate subnational measles vaccination coverage in high-burden settings, such as in Ethiopia. However, the distribution of remaining susceptible individuals, either unvaccinated or having never previously been infected, across age groups and subnational geographies is unknown. In this study, we developed a dynamic transmission model that incorporates geospatial estimates of routine measles vaccination coverage, available data on supplemental immunization activities, and reported cases to estimate measles incidence and susceptibility across time, age, and space. We use gridded population estimates and subnational estimates of routine and supplemental measles vaccination coverage. To account for mixing between age-groups, we used a synthetic contact matrix, and travel times via a friction surface were used in a modified gravity model to account for spatial movement. We explored model fitting using Ethiopia as a case study. To address data-related and statistical challenges, we investigated a range of model parameterization and possible fitting algorithms. The approach with the best performance was a model fitted to case notifications adjusted for case ascertainment by using maximum likelihood estimation with block coordinate descent. This strategy was chosen because many data observations (and likely presence of unquantified uncertainty) yielded a steep likelihood surface, which was challenging to fit using Bayesian approaches. We ran sensitivity analyses to explore variations in vaccine effectiveness and compared patterns of susceptibility across space, time, and age. Substantial heterogeneity in reported measles cases as well as susceptibility persists across ages and second-administrative units. These methods and estimates could contribute towards tailored subnational and local planning to reduce preventable measles burden. However, computational and data challenges would need to be addressed for these methods to be applied on a large scale.