Mathematical Biosciences and Engineering

With significant population fractions in many societies who refuse vaccines, it is important to reconsider how vaccination is incorporated into compartmental epidemiology models. It is still most common to apply the vaccination rate to the entire class of susceptibles, rather than to use the more realistic assumption that the vaccination rate function should depend only on the population of susceptibles who are willing and able to receive a vaccination. This study uses a simple generic disease model to address two questions: (1) How much error is introduced in key model outcomes by neglecting vaccine unwillingness?, and (2) Can the error be reduced by incorporating vaccine unwillingness into the vaccination rate constant rather than the rate diagram? The answers depend greatly on the time scale of interest. For the endemic time scale, where longterm behavior is studied with equilibrium point analysis, the error in neglecting unwillingess is large and cannot be improved upon by decreasing the vaccination rate constant. For the epidemic time scale, where the first big epidemic wave is studied with numerical simulations, the error can still be significant, particularly for diseases that are relatively less infectious and vaccination programs that are relatively slow.

Polygenic risk scores (PRSs) quantify an individuals genetic susceptibility to complex traits and diseases. Conventional PRSs, which are based on linear models, perform poorly for phenotypes with skewed distributions or with genetic effects that vary across the distribution. We propose a quantile regression-based PRS (QPRS) that can capture quantile-specific genetic effects. While existing PRSs provide only a single score, QPRS models genetic influences at multiple quantiles of the phenotype, thereby enhancing predictive performance by utilizing these multiple scores as covariates. We evaluate the performance of our method through both simulations and a real-data application. In simulations, QPRS significantly reduces the mean squared error (MSE) compared to the conventional PRS, both in the presence of variance quantitative trait loci and outliers. For real data analysis, we use data from Korea Genome and Epidemiology Study (KoGES) to evaluate predictive performance. We consider two prediction tasks: a continuous outcome (glucose level) and a binary outcome (diabetes status, derived from glucose level). For glucose-level prediction, the model incorporating QPRS achieves a R2 value 4.69 times higher than the model using conventional PRSs. For predicting diabetes status, the model with QPRS produces an area under the curve 1.06 times higher than the model with conventional PRSs.

Cervical cancer remains a significant cause of mortality and economic burden, particularly in developing countries with low rates of human papillomavirus (HPV) vaccination and screening. To address this, we present a mathematical model for controlling cervical cancer by integrating strategic HPV vaccination, screening and treatment. The population is divided into seven compartment: susceptible, vaccinated, infected with HPV, screened, cervical cancer, under treatment, and recovered. The models well-posedness is first established by proving the boundedness and non-negativity of solutions, ensuring biological relevance. The basic reproduction number R0 is computed using the next-generation matrix. The local and global stability of the disease-free equilibrium is analysed using the Jacobian matrix and Lyapunov function respectively. Furthermore, bifurcation analysis is performed using the Castillo-Chavez and Song theorem and sensitivity analysis is conducted on key parameters to identify their influence on disease dynamics. Numerical simulations of the model supports the analytical results. The findings of the study indicate that if the reproduction number is less than one, the solution converges to the disease-free state, signifying the asymptotic stability of the HPV-Cervical cancer free steady state. Crucially, the model demonstrates that increasing vaccination, screening and treatment rates significantly reduces HPV and cervical cancer incidence. This study underscores the value of mathematical modeling in informing the public health policy and provides a framework for optimizing control measures against HPV and Cervical cancer.

To characterize tuberculosis transmission and assess the impact of important interventions, a data-driven SEITR TB model is created. The potential for disease persistence has been calculated using the basic reproduction number. To determine the factors most significantly affecting the spread of tuberculosis, stability and sensitivity analyses are conducted. Strengthened treatment measures and optimized distancing significantly lower infection levels, according to numerical simulations. The Least Squares Fitting technique is used to validate real epidemiological data with a model solution. And the results emphasize that the best combinations of social distancing and treatment not only reduce the number of infections but also provide a cost-effective strategy for public health planning. Additionally, two numerical techniques, namely Pearson correlation and Partial Rank Correlation Coefficients (PRCC), are utilized to assess the sensitivity of model parameters. It is noted that the outcomes of these two methods are in agreeable comparison with one another regarding sensitivity analysis.

Infectious diseases and chronic diseases are two major fields in epidemiology that have traditionally been studied separately because of their distinct etiologies and modeling methods. Infectious disease data are typically collected at an aggregated level and analyzed using compartmental models, most commonly the susceptible (S), infectious (I), and recovered (R) (SIR) model, whereas chronic disease data are usually collected at the individual level and analyzed using multi-state survival models. Previous studies have pointed out the link between compartmental models and survival analysis by reconstructing the aggregated infection disease data into individual-level data. However, these studies have largely focused on the two-state transition from S to I state, and few studies have simultaneously modeled the three-state process, S, I, and R. In this paper, we propose to use a discrete-time multi-state framework to model the three-state progression of infectious disease. We first introduce and compare the underlying methodological foundations for modeling infectious disease and chronic disease dynamics, then show the link between compartment models and multi-state models, and finally present how infectious disease can be modeled using the multi-state framework under the two scenarios: 1) all S, I, and R states are observed, and 2) only the I state is observed, with the R state treated as latent. In the application, we applied the multi-state approach to estimate the dynamics of influenza using the data in a British boarding school in 1978, where only the infected cases were observed over time. The estimated recovery rate was 0.42 and the corresponding contact rate was0.91 (95% CI: 0.84, 0.98). The basic reproductive number was 2.17 (95% CI: 2.00, 2.33), which declined to approximately 1 by day 6, and continued to decrease thereafter. Overall, we propose a unified multi-state approach for modeling infectious and chronic disease progression, which may provide evidence to inform timely and effective infectious disease prevention.

Lassa Fever control remains a daunting task for authorities in poorly resourced settings where the costs of implementing the control strategies remain high as the disease has multiple hosts and environmental spread. An important metric based on community pathogen load may be useful in estimating the level of control over all in the community in order to budget for the costs of control effectively. We developed a model that accounts for the community contribution of Lassa viral load in humans, rodents as well as the environment accounting for Community Pathogen Load incorporating three control strategies. The model was calibrated and fitted to the Nigerian data and optimized to establish the most cost-effective strategy using cost-effective analysis. Our results suggested that targeting the human community pathogen load remains an important control focus but the control of rodent contribution was equally important. Overall, the combination of three control strategies was the best control measure that is cost-effective for curbing Lassa fever in the population.

This paper looked at the exploration of Lassa fever transmission dynamics through stochastic models which yielded valuable insights into the interplay of factors influencing the probability of extinction and persistence of the virus within a population. By embracing the inherent randomness and variability in the system, the model provided a more realistic representation of the complex ecological and epidemiological dynamics of Lassa fever. We developed the deterministic model using a system of ordinary differential equations and the stochastic model using the Continuous Time Markov Chain. The probability of extinction and persistence underscored the need for a proactive and flexible approach to public health management. Our study revealed that introducing Lassa virus at the onset of an epidemic through various routes affects the likelihood of pathogen extinction. The presence of multiple infection routes increased the probability of pathogen persistence, highlighting complex transmission dynamics. Variations in contact rates, particularly between susceptible rodents and the environment community pathogen load, play a crucial role in influencing pathogen dynamics. This interconnected nature of transmission pathways underscores the factors governing Lassa virus persistence or extinction in a population, providing valuable insights for targeted management and control strategies for Lassa fever.

This study presents a theoretical and mathematical framework for understanding the dynamical behavior of infectious disease spread using a compartmental modeling approach. The proposed model incorporates memory effects to capture temporal dependencies that are not adequately represented by classical formulations. Qualitative analysis is employed to investigate the stability properties of the system and the role of key mechanisms in shaping long term dynamics. Publicly available surveillance information is used only to illustrate the consistency of the model behavior with observed trends. The results highlight the value of memory based modeling structures for describing complex biological processes and provide a general mathematical perspective for studying epidemic dynamics.

Nipah virus (NiV) is a sporadic yet extremely deadly zoonotic pathogen, with reported case fatality rates of 40%-75% in impacted areas. Prolonged incubation, documented relapse, and delayed-onset encephalitis following apparent recovery indicate that NiV dynamics are influenced by intricate temporal processes. However, mechanistic contributions of these processes to epidemic persistence remain poorly understood. In this study, we develop and analyze a delay differential equation model for NiV transmission that explicitly incorporates incubation delay, relapse, and post-recovery delay effects. We compute a primary-transmission reproduction threshold (R0), characterize the disease-free and endemic equilibria, and analyze their stability, including delay-induced Hopf bifurcations. We show that relapse modifies the endemic-equilibrium existence condition, so an endemic equilibrium is not determined solely by the classical threshold criterion R0 = 1. We calibrate the model to NiV incidence data from Bangladesh (2001-2024) and perform simulations and sensitivity analyses to evaluate the effects of relapse and delays across epidemiological scenarios. Results indicate that sustained oscillations occur only under hypothetical parameter regimes, suggesting that delay-induced periodic outbreaks are unlikely under empirically informed conditions. Scenario analyses demonstrate that relapse and encephalitis-related delays predominantly influence post-peak dynamics, while incubation delay alters the time and intensity of the epidemic peak. We also introduce a relapse-driven replenishment fraction to quantify contribution of relapse to continued transmission, demonstrating its growing significance following the first outbreak peak. Overall, our results identify relapse as a key mechanism for epidemic persistence and underscore the importance of incorporating relapse and biological time delays into epidemiological modeling and public health strategies.

The COVID-19 pandemic has presented severe challenges in understanding and predicting the spread of infectious diseases, necessitating innovative approaches beyond traditional epidemiological models. This study introduces an advanced method for automated model discovery using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, leveraging a dataset from the COVID-19 outbreak in Thuringia, Germany, encompassing over 400,000 patient records and vaccination data. By analysing this dataset, we develop a flexible, data-driven model that captures many aspects of the complex dynamics of the pandemics spread. Our approach incorporates external factors and interventions into the mathematical framework, leading to more accurate modelling of the pandemics behaviour. The fixed coefficient values of the differential equation as globally determined by the SINDy were not found to be accurate for locally modelling the measured data. We therefore refined our technique based on the differential equations as found by SINDy, by investigating three modifications that account for recent local data. In a first approach, we re-optimized the coefficient values using seven days of past data, without changing the globally determined differential equation. In a second approach, we allowed a temporal dependence of the coefficient values fitted using all previous data in combination with regularization. As a last method, we kept the coefficients fixed to the original values but augmented the differential equation with a small neural network, locally optimized to the data of the past week. Our findings reveal the critical role of vaccination and public health measures in the pandemics trajectory. The proposed model offers a robust tool for policymakers and health professionals to mitigate future outbreaks, providing insights into the efficacy of intervention strategies and vaccination campaigns. This study advances the understanding of COVID-19 dynamics and lays the groundwork for future research in epidemic modelling, emphasising the importance of adaptive, data-informed approaches in public health planning.

Influenza forecasting in (sub-)tropical regions remains understudied due to year-round, irregular transmission patterns. Further, the variation in seasonality and transmission characteristic of influenza in post-COVID-19 pandemic could be attributed to various drivers to quantify for better understanding. To address this issue, this study introduced an ensemble forecasting approach that incorporates varied dataset lengths to forecast influenza activity in Hong Kong, integrating multi-stream surveillance data, including absolute humidity, temperature, ozone, and school closures/holidays. We applied temporal cross-validation to evaluate forecasting performance for short- and long term separately across different training-sets and model variants, ultimately constructing ensemble forecasts weighted by individual model performance. The optimal ensemble model could forecast the 2019/20 winter influenza season onwards and evaluate the impact of COVID-19 public health and social measures (PHSMs). We further extended the framework to forecast influenza in post-pandemic period since March 2023, accounting for the impact of cessation of PHSMs and COVID-19-induced cross-protection/competition in population susceptibility. Forecasts showed two peaks in 2019/20 season, which could account for 95.2% (95% prediction interval (PI): 89.1%, 98.3%) reduction in attack rate for COVID-19 PHSMs. The post-pandemic forecasts indicated changes in influenza transmission dynamics and seasonality, highlighting the need to consider factors such as population immunity and co-circulation with COVID-19 in future influenza forecasts. This study emphasizes the importance of incorporating diverse factors for better influenza forecasts in (sub-)tropical regions. The proposed framework offers a scalable tool for forecasting other respiratory virus transmissions, supporting healthcare agencies in managing future infection burdens and enhancing preparedness. Author summaryReliable and proactive forecasts of influenza activity and timing of epidemic outcomes enable public health officials to plan targeted responses. However, unlike temperate locations, the irregular seasonality of influenza in tropical/subtropical locations leads to highly variable forecasting patterns when models use varying lengths of historical data, reducing the robustness of forecasts. By leveraging multi-stream surveillance data in Hong Kong, we developed a mechanistic model-based ensemble forecasting framework that integrate potential combinations of data and models for short-, medium-, and long-term forecasts of influenza outcomes. Beyond methodological advancement, this framework has broader implications in assessing the impact of COVID-19-related interventions on influenza dynamics during pandemic and evaluating potential co-circulation risk of respiratory viruses including influenza and COVID-19 in post-pandemic era.

Schistosomiasis is a neglected parasitic disease caused by various trematode species of the genus Schistosoma for which 251 million people needed treatment in 2021. Many mathematical models of Schistosoma mansoni transmission incorporate the effect of chemoprophylaxis on parasite burden within the human host. While praziquantel is the most commonly implemented pharmaceutical used to control schistosomiasis, due to its applicability over several species and its negligible side effects, it is not very effective against juvenile schistosomes in humans. This limited efficacy on the juvenile life-stage of the parasite may be an important factor in the persistence of the disease. The demographic consequences of praziquantel use on schistosome population age and sex composition within the human host may obfuscate the effectiveness of these chemoprophylactic control strategies. Furthermore, the effectiveness of this treatment is heavily dependent on the force of infection to humans and the frequency at which these pharmaceuticals are administered. Using a stochastic mechanistic model, we investigated the effects of inconsistent drug efficacy among parasite life stages, varying parasite population structure within the human host, and alternative treatment regimes to the prevailing once-yearly strategy. This allowed us to identify the reduction in infection prevalence under differing infection risk scenarios, parasite population structures at the time of treatment, and treatment schedules. Our results indicate that if elimination is the goal, then widespread (>75% of the population) treatment should be the target and that more frequent treatment schedules are useful up to several treatments a year.

The two largest US measles outbreaks in over two decades (2025 Gaines County, Texas: 414 cases, contained; 2025-2026 Spartanburg County, South Carolina: 923+ cases, ongoing) occurred in counties with similar sub-threshold K-12 MMR coverage (85.1% vs 88.8%), yet their trajectories diverged dramatically. Using kernel density estimation with a common bandwidth and bootstrap uncertainty quantification, we compared sub-county vaccination data at the district level for Texas (3 districts, 3,560 students) and the school level for South Carolina (93 schools, 57,281 students). Peak susceptible density in Spartanburg County was 5.7 times that of Gaines County (23 vs. 4 unvaccinated students per square mile; 95% CI 2.4-12.5, non-overlapping). In Texas, a single isolated cluster around Seminole ISD limited spatial connectivity, producing self-limiting spread. In South Carolina, a northwest corridor of under-vaccinated schools created overlapping catchment areas that sustained transmission chains. These findings demonstrate how county-level aggregates can mask nearly six-fold differences in local risk, underscoring the need for school-level spatial surveillance.

Background/AimMalaria, in Nigeria, is a disease of public health concern that has caused both morbidity and mortality, with the highest prevalence in Kebbi State. Long-lasting insecticidal nets (LLINs) have been instrumental in controlling the burden of the disease. This study aims to assess the effect of LLINs on malaria transmission dynamics in Kebbi State, Nigeria. MethodsRoutine data for the confirmed uncomplicated malaria cases in Kebbi State, Nigeria, from January 2015 to May 2024 were used to understand the transmission dynamics within the population. A deterministic model was developed to capture the malaria transmission dynamics in Kebbi State. Qualitative analysis was carried out, establishing the positivity and boundedness of solutions to ensure the biological feasibility of the model. The disease-free equilibrium was analyzed for stability, revealing under which condition the disease is eradicated. Effective reproduction number, [R]e, was derived, governing the disease persistent in the presence of intervention. The endemic equilibrium was further examined to indicate situations where the disease persist in the population. The model was fitted to Kebbi state monthly malaria cases using the least squares estimation method implemented in R. Numerical simulations were performed using the R software. Prediction scenarios of malaria cases considering different usage levels of LLINs (38.2%, 50% and 80%) are visualised through the simulation of the malaria model. ResultsThe result showed that if there had been 80% sustained level LLINs usage as proposed by NMEP since 2015, there would have been about 5.2 million malaria cases averted, which corresponds to 97.98% reduction. However, moving forward, if 80% usage can be achieved and sustained, about 3 million malaria cases would be averted by May 2029, signifying an impressive reduction of 78.93% in incidence. ConclusionWe conclude that in order to significantly reduce malaria incidence in Kebbi State to its bearest minimum, health policymakers and decision makers in Nigeria should prioritise scaling up LLINs usage in the State by expanding LLINs distribution and improving malaria education in the .

Human African Trypanosomiasis (HAT) remains a persistent public health threat in sub-Saharan Africa, with transmission dynamics tightly coupled to the ecology and physiology of its tsetse fly vector. Despite growing evidence that temperature strongly modulates vector survival, development, and biting behavior, most existing transmission models assume static environmental conditions. We develop a model for HAT that incorporates temperature-dependent vector recruitment, mortality, and biting rates, thereby mechanistically linking environmental variability to epidemiological outcomes. The model couples human and tsetse populations and admits both disease-free and endemic equilibria. Using the next-generation matrix approach, we derive an explicit expression for the basic reproduction number and show that it depends nonlinearly on temperature through multiple entomological pathways. Bifurcation analysis reveals a forward transcritical bifurcation, indicating a clear threshold for disease persistence. Our findings demonstrate how temperature can fundamentally alter transmission potential and control thresholds, highlighting the importance of integrating climate-sensitive vector biology into HAT risk assessment and intervention planning under ongoing environmental change.

In 1798, Jenners smallpox vaccine made it possible to prevent the deadliest of childhood diseases. In Denmark the vaccine was used from 1801, and by 1810 a mandatory 1-dose childhood vaccination program was instituted, free of charge. As proof of vaccination (or natural immunity) was required for church confirmation around age 13, about 90 % of children were vaccinated and smallpox disappeared from Copenhagen after 1808. After a 16-year "honeymoon period", it returned in 1824 with a new face: a milder disease in mostly young adults (1, 2). Here we investigate the effects of smallpox vaccination on the epidemic patterns through the post-honeymoon era (1824-1875). We accessed data from the hospital "Sokvaesthuset" where all smallpox cases, mild and severe, were hospitalized during 1824-1835 in order to contain the outbreak. We identified [~]3000 smallpox cases and four separate epidemics occurring during this period (1-3). We used a mechanistic model (SEIR) to assess factors playing a role in explaining the return of smallpox, and the changing age distribution. These factors included vaccination coverage, duration of immunity from vaccination and from natural infections, and the fate of the "lost generation" of persons born around 1800, too early to get vaccinated and too late to have been infected with smallpox. Our model tracks well the disappearance and return of smallpox in 1824, the interval between epidemic peaks, and the aging pattern. We propose vaccine waning after [~]20 years as the primary reason explaining the return of smallpox and the epidemic pattern. SignificanceSmallpox has played a major role in shaping modern medicine. Recently, it has received renewed attention due to fears of bioterrorism and the emergence of the closely related mpox. In this article, we use data from the carefully recorded smallpox outbreaks in Copenhagen in the 1800s to study its dynamics following vaccine rollout. We show that the vaccine likely induced a long-lived but finite immunity and that the "lost generation" who were neither vaccinated nor had contracted smallpox in childhood continued to be plagued by the disease in the following decades. The study is relevant for understanding how smallpox was eradicated and the role of vaccination in dealing with present epidemic threats.

Monkeypox viral disease has been and continues to be a global public health concern. Currently, there are existing, though minimal measures to manage mpox and any future outbreaks. Relying on data-driven modeling for early detection of mpox and prediction of possible cases and deaths in the presence of an outbreak is thus imperative. The present study forecasted global mpox virus cases and deaths in Asia, Africa, Australia, Europe, North America, Oceania, and South America. Three forecasting models (deep neural network, gradient boosting, and polynomial regression) were trained on data from the seven geographical regions. The performance of the three models was assessed using coefficient of determination, mean squared error, root mean squared error, and mean absolute scaled error across each region. Prediction using the deep neural network revealed a potential of higher mpox deaths in Africa and higher mpox cases in South America. Prediction using gradient boosting showed a potential of mpox deaths in Africa and higher mpox cases in Asia and North America. Prediction using polynomial regression revealed a potential of higher mpox deaths in Africa and Asia while rapid rises in mpox cases from 2025 to 2028 were anticipated in all regions except Asia in case of a monkeypox outbreak. For the three models, the tree-based ML model (gradient boosting) outperformed the statistical model and deep learning model by R2 and MSE in predicting mpox case counts across all the seven geographical regions. This study showcases the worth in using data-driven modelling to predict emerging and re-emerging infectious diseases such as mpox.

Collective interaction of individuals in various settings is crucial for exposure to infections, encompassing complex viral interplay and amplifying infectious risk through phenomena such as social reinforcement, clustering and superspreading events, during the COVID-19 pandemic. However, standard epidemic models often inadequately capture such heterogeneity, overlooking the higher-order social structural. Spatiotemporal variation in transmission, an essential feature of the pandemic, remains poorly quantified at various scales, particularly in integrating high-resolution data streams and complex network approaches. We introduced a higher-order simplicial model that unifies human mobility data, genetic diversity and antigenic drift to systematically investigate the role of social reinforcement, spatiotemporal variation and genetic mutations in SARS-CoV-2 transmission. We found a median of 5.3% to 14.4% of infections across provinces were attributed to social reinforcement, while cluster heterogeneity contributed to a median of 17%-71% increase in susceptibility. Multiple viral interactions elevated transmissibility by 68%-70% across the periods of dominant variants. The reconstructed transmission networks underscored distinct spatiotemporal variation, with dynamic critical locations, varying mobility patterns, and evolving geographic cluster structures, by assessing complex networks. The influence of human mobility was found to be positive on transmission, effective distance was negatively associated with infection risks, while greater genetic diversity and antigenic drift were linked to higher susceptibility and transmissibility. Our proposed data-driven higher-order framework could help us to understand epidemics better by accounting the role of collective interactions, population mobility, and genetic mutation in transmission, which could inform the targeted interventions to mitigate SARS-CoV-2 and other respiratory pathogens.

Measles resurgence in high-income countries that previously achieved elimination reveals a critical surveillance failure: current systems rely on county-level aggregates that obscure fine-scale clustering where outbreaks originate. We assembled the nationwide multiscale vaccination database spanning 45 US states (2013-2025), encompassing over 50,000 schools, 13,000 districts, and 3,000 counties. We developed a gravity-based transmission framework and demonstrate that school-level effective reproduction numbers crossed the epidemic threshold in 2022-2023, a transition invisible to aggregated surveillance. Average susceptibility doubled from approximately 5% to 10% following the COVID-19 pandemic. Three independent mechanisms drive aggregation bias: enrollment-weighted averaging systematically dilutes small under-vaccinated schools; gravity kernels attenuate transmission potential with coarser spatial scales; and clustering signal erasure converts heterogeneous risk landscapes into falsely uniform county averages. School district boundaries frequently misalign with counties, creating cross-boundary transmission corridors that push well-vaccinated counties above epidemic threshold through spillover alone. State trajectories diverge markedly, shaped by exemption policies and local infrastructure. Preventing measles re-endemicity requires surveillance systems operating at the spatial scale where vulnerability accumulates.

In this research, we create a new fractional-order SEIHRD framework to examine how the Nipah virus moves from one species to another (zoonotic spillover) and how it later spreads throughout a community (via contact with one another) or in a hospital or isolation situation (via entering into a hospital or being placed under quarantine). We used the fractional-derivative formulation of the SEIHRD model to demonstrate memory-based effects related to the progression of an infection and also reflect time-distributed effects associated with surveillance and control measures placed on an infected patient. We first demonstrated that the basic epidemiologic properties of the model were consistent by showing that the solutions of the SEIHRD differential equations will always yield positive and bounded solutions within biologically relevant parameter ranges. We then established the well-posedness of this model by transforming the SEIHRD differential equations into an equivalent integral operator and applying various fixed-point arguments to demonstrate that there will always be unique solution(s) to the SEIHRD differential equations. To evaluate the threshold parameter for the transmission of Nipah virus within a given population we calculated the threshold level through the next generation method to determine the expected number of secondary infections from a new or chronically infected host. One of the main contributions of this work is to include an analysis of the robustness of a given solution to all potential perturbations (i.e., Ulam-Hyers and generalized Ulam-Hyers stability). In addition, we provide analytic results guaranteeing that small perturbations due to approximate modeling, numerical approximation (discretization), or the lack of data fidelity will produce controlled deviations in the solutions. To finish this project, we perform a global sensitivity analysis on uncertain coefficients to evaluate their contribution to the uncertainty of each coefficient and to find out the coefficients that most strongly influence major outcome metrics. This will allow us to develop a priority order for prioritizing spillover control (reduction of human contact and/or isolation), contact reduction, and expenditure of resources towards isolation-related interventions. The resulting framework converts fractional epidemic modeling from a descriptive simulation to a replicable method with robustly defined behavior and equal response prediction.