Mathematical Biosciences and Engineering

The left ventricle (LV) exhibits torsional deformation during systole, and mechanical relaxation begins during the isovolumic phase. Recent advances in imaging techniques, such as MRI, have revealed that myocardial tissue deformation and sarcomere length changes occur during the isovolumic relaxation phase, even when the chamber volume remains constant. Although such ventricular deformation during the isovolumic phase is considered important for blood ejection and filling efficiency, its mechanistic contribution to contraction and relaxation remains unresolved. In this study, we hypothesized that sarcomere length dynamics during the isovolumic phase affect the isovolumic contraction and relaxation time (IVCT and IVRT) by regulating the contraction force via the force-velocity relationship of ventricular myocytes. To investigate this hypothesis, we focused on experimentally reported differences in the relationship between sarcomere length and LV volume across the endocardial and epicardial layers, as described by Rodriguez et al. We constructed and compared two types of hemodynamic models within the same integrated framework consisting of a circulation model, a LV model, and a myocardial cell contraction model by Negroni-Lascano et al., which differ only in how sarcomere length is determined: a volume-based length model (VL model), in which sarcomere length is uniquely determined by LV volume, and a volume-force-coupled length model (VFL model), in which sarcomere length is determined by the balance between LV volume and contraction force. Simulation results showed that in the VFL model, compared to the VL model, sarcomere length changed during the isovolumic phase, leading to a decrease in contractile force and shortening of IVRT, which may contribute to improved hemodynamic efficiency. These results indicate that sarcomere length dynamics can mechanically regulate force decay during isovolumic relaxation, even under constant left ventricular volume. This study provides a theoretical framework for understanding the contributions of different layers within the LV wall to diastolic function during the isovolumic relaxation phase.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has continuously evolved since its emergence in the human population in 2019. As of 1st August 2025, more than 1,700 Omicron subvariants have been designated by the Pango nomenclature system. The Pango nomenclature system designates a new lineage based on genetic and epidemiological information of SARS-CoV-2 strains. However, there is a possibility that strains that have similar genetic backgrounds and the same phenotype are given different Pango lineage names. In this paper, we propose a new algorithm, called FindPart-w, which can identify groups of viral lineages that share the same relative effective reproduction numbers. We introduced a new lineage replacement model, called the constrained RelRe model, which constrains groups of lineages to have the same relative effective reproduction numbers. The FindPart-w algorithm searches the equality constraints that minimise the Akaike Information Criterion of constrained RelRe models. Using hypothetical observation count data created by simulation, we found that the FindPart-w algorithm can identify groups of lineages having the same relative effective reproduction number in a practical computational time. Applying FindPart-w to actual real-world data of time-stamped lineage counts from the United States, we found that the Pango lineage nomenclature system may have given different lineage names to SARS-CoV-2 strains even if they have the same relative effective reproduction number and similar genetic backgrounds. In conclusion, this study showed that viruses that had the same relative effective reproduction number were identifiable from temporal count data of viral sequences. These findings will contribute to the future development of lineage designation systems that consider both genetic backgrounds and transmissibilities of lineages.

Human immunodeficiency virus (HIV) persistence remains a major barrier to cure due to the existence of long-lived latent reservoirs that evade immune clearance and persist despite combination antiretroviral therapy (ART). Although ART effectively suppresses viral replication, treatment interruption often leads to rapid viral rebound originating from these latent reservoirs. In this study, we develop a deterministic mathematical model describing the in vivo dynamics of HIV infection incorporating uninfected CD4+ T cells, infected cells, latent reservoirs, deep latent reservoirs, and infectious and non-infectious virions, while explicitly accounting for the therapeutic effects of reverse transcriptase inhibitors (RTIs), protease inhibitors (PIs), and Tat transcription inhibitors. Analytical results establish positivity and boundedness of solutions and derive the effective reproduction number Re using the next-generation matrix approach. Stability analysis shows that the virus-free equilibrium is locally asymptotically stable when Re < 1, while viral persistence occurs when Re > 1. Numerical simulations were performed to investigate therapy interactions, viral rebound following treatment interruption, and the impact of drug efficacy on viral set-points and latent reservoir dynamics. To further explore therapy interactions, three-dimensional viral set-point surfaces and heat maps were generated to examine how combinations of infection inhibition, viral production inhibition, and transcriptional inhibition influence viral dynamics. The simulations reveal that Tat inhibition suppresses viral transcription, thereby reducing the transition of infected cells into productive infection and limiting viral propagation when combined with conventional ART mechanisms. The therapy parameter planes further demonstrate that strong transcriptional inhibition promotes the transition of infected cells into deep latency, supporting the emerging block-and-lock strategy for functional HIV cure. In addition, a three-dimensional eradication boundary surface and therapy cube were constructed to identify regions of parameter space where Re < 1, corresponding to successful viral control. These visualizations show that viral eradication is unlikely when therapies act independently but becomes achievable when multiple therapeutic mechanisms act simultaneously. Overall, the results highlight the critical role of transcriptional inhibition through Tat-targeting therapies in complementing existing ART regimens. By simultaneously suppressing viral replication and promoting deep latency, Tat-based combination strategies may significantly reduce viral rebound and contribute to long-term functional control of HIV infection.

This paper presents a unified six-state Continuous-Time Markov Chain (CTMC) framework for Chronic Kidney Disease (CKD) progression, with CKD stages 1-5 modeled as transient states and death as an absorbing state. Under a non-homogeneous CTMC formulation, we derive integral representations for transition probabilities, state distributions, sojourn times, and survival-related quantities. We then study the homogeneous case as a tractable baseline and provide explicit formulas for key quantities. Although the methodology is rooted in standard multi-state theory, these expressions are often left implicit in applied analyses; here they are written out explicitly within a unified CKD framework. We construct covariate-dependent transition rates through a proportional hazards structure, using the standard identification of cause-specific hazards with CTMC transition rates. We fit the time-homogeneous baseline model to 335,283 longitudinal observations from 21,100 synthetic electronic health record patients by maximum likelihood. In this synthetic cohort, the covariate model improves held-out log-likelihood per transition over the null model, with stable performance across 10-times-repeated 5-fold cross-validation, and reproduces the main population-level prevalence patterns. The transition-specific estimates can also be translated into sojourn-time and survival summaries. The model suggests that male sex is associated with faster progression across nearly all CKD transitions, and that hypertension shows a stage-dependent association, with lower estimated transition rates in early stages but a substantial acceleration of the Stage 4 to Stage 5 transition. Overall, the proposed framework provides a mathematically explicit approach for studying CKD trajectories from longitudinal health records.

Against the backdrop of global climate change and accelerating population mobility in 2025, chikungunya fever (CHIKF) exhibited a trend of worldwide spread, significantly increasing the difficulty of controlling tropical mosquito-borne diseases. To enhance the precision of intervention strategies, this study developed an age- and sex-structured human-mosquito interaction dynamic model based on data from the largest CHIKF outbreak ever recorded in China, and conducted a targeted analysis of prevention and control strategies. By decomposing the basic reproduction number and examining population heterogeneity, asymptomatic males aged 15-59 years were identified as the core transmission group. Optimal control analysis revealed that the synergistic implementation of three measures-- reducing the effective human-to-mosquito transmission rate, reducing the effective mosquito-to-human transmission rate, and suppressing mosquito population density--could reduce the overall infection rate by 95.7586%. Among these, mosquito population suppression should be prioritized as a universal core strategy; however, its protective effect on females aged 60 years and above was relatively weak, warranting particular attention. The study further demonstrated that asymmetric intensity combinations targeting these three intervention pathways--such as intensity profiles of "10%, 90%, 90%" or "60%, 80%, 90%"--could achieve effective outbreak control. This research elucidates population-specific transmission patterns and key pathways for intervention intensity, providing a theoretical and strategic foundation for the precise control of mosquito-borne diseases. It also provides actionable operational insights to support rapid response and strategy optimization for future emerging outbreaks. Author summaryCHIKF is a mosquito-borne viral disease that is gradually spreading from tropical regions to other areas. To achieve more precise control of this disease, we developed an age- and sex-structured analytical model based on the largest CHIKF outbreak in China, aiming to provide a scientific basis for responding to potential future outbreaks with inherent uncertainties. The study found that asymptomatic males aged 15-59 years were the primary drivers of transmission and should be prioritized as a key population for reducing viral spread in prevention efforts. When evaluating the effectiveness of different intervention strategies, females aged 60 years and above were the least affected by the implemented measures, indicating that this group should strengthen personal protection to lower their infection risk. Among all control measures, mosquito suppression was the most effective, suggesting that vector control strategies should be prioritized in future outbreak responses.

To meet the growing demand for precision and intelligent agricultural management, crop simulation models offer substantial potential for optimizing farm planting strategies. By simulating crop growth processes and assessing the effects of different management practices, these models provide a scientific basis for planting decision-making. In this study, the DSSAT model was first used to optimize the planting strategies of Farm X in 2023. Based on the optimized plans, the model was further applied to predict crop yields per unit area for 2024 and to establish the relationships among yield, planting density, and fertilizer application rate. Subsequently, SPSS was employed to develop a regression model describing the relationship among net profit per unit area, planting density, and fertilizer application rate. A genetic algorithm was then used to identify the optimal solutions under different scenarios, generating prescription maps for the optimal planting density and fertilizer application rate for each plot of Farm X in 2024. The results provide a scientific reference for the mechanized and automated implementation of field management practices and support the dual optimization of economic returns and resource use efficiency. This study not only conducted a systematic optimization of Farm X planting strategies for 2023, but also provided detailed predictions and optimized prescriptions for 2024 in a visual and practical form. The proposed approach offers a scientific decision-support tool for farm planting strategy formulation and lays a foundation for the intelligent and automated development of modern agriculture.

Within many bacterial colonies, persister cells exist as a subpopulation that is tolerant to antibiotics and other stressors, yet not genetically distinct from the rest of the colony. A recent study has proposed epigenetic inheritance as a mechanism that leads to the presence of persister cells. We analyze a nonlocal PDE-ODE model introduced in that study to describe the epigenetic inheritance process and establish its mathematical well-posedness, including existence, uniqueness, and nonnegativity of solutions. We identify a sharp parameter threshold delineating extinction from persistence of the colony: below this threshold the washout equilibrium is globally asymptotically stable, while above it a unique positive equilibrium exists and the population is weakly persistent. Notably, this threshold is independent of the internal community structure.

Variability in gene expression among single cells and growing cell populations can arise from the stochastic nature of protein synthesis, which often occurs in random bursts. This study investigates the variability in the expression of a growth-sustaining protein, whose concentration is regulated by a negative feedback loop due to cell growth-induced dilution. We model the distribution of protein concentration using a Chapman-Kolmogorov equation for single cells and a population balance equation for growing cell populations. For single cells, we derive an explicit solution for the protein concentration distribution in state space and represent it as a Bessel function in Laplace space. For growing populations, we find that the distribution satisfies a Heun differential equation with singular boundary conditions. By addressing the central connection problem for the Heun equation, we quantify the population-level protein distribution and determine the Mathusian parameter, which characterizes population growth. This work provides a comprehensive analytical framework for understanding how stochastic protein synthesis impacts gene expression variability and population dynamics.

Mass-conserved reaction-diffusion systems are used as mathematical models for various phenomena such as cell polarity. Numerical simulations of this system present transient dynamics in which multiple stripe patterns converge to spatially monotonic patterns. Previous studies indicated that the transient dynamics are driven by a mass conservation law and by variations in the amount of substance contained in each pattern, which we refer to as "pattern flux". However, it is challenging to mathematically investigate these pattern dynamics. In this study, we introduce a reaction-diffusion compartment model to investigate the pattern dynamics in view of the conservation law and the pattern flux. This model is defined on multiple intervals (compartments), and diffusive couplings are imposed on each boundary of the compartments. Corresponding to the transient dynamics in the original system, we consider the dynamics around stripe patterns in the compartment model. We derive ordinary differential equations describing the pattern dynamics of the compartment model and analyze the existence and stability of equilibria for the reduced ODE with respect to the boundary parameters. For a specific parameter setting, we obtained results consistent with previous studies. Moreover, we present that the stripe patterns in the compartment model are potentially stabilized by changing the parameter, which is not observed in the original system. We expect that the methodology developed in this paper is extendable to various directions, such as membrane-induced pattern control.

Experimental studies show that tumor cells adopt migratory or proliferative phenotypes depending on the local extracellular matrix (ECM). In this work, we propose a minimal go-or-grow invasion model, comprising two specialist cell phenotypes: proliferating and migratory, with phenotypic switching and cell migration depending on local ECM density. Numerical simulations of this model reveal that the spatial arrangement of proliferative and migratory cells depends on the choice of phenotypic switching function. We then ask whether this specialist cell-phenotype model can be reduced to a generalist cell-phenotype model. We derive a relationship between the reduced model and go-or-grow model in the fast phenotypic switching regime. We observe that the reduced model captures the dynamics of the original model, for a range of realistic phenotypic switching functions. We analytically derive the minimum traveling wave speed of the reduced model in a homogeneous ECM bed. Moreover, using linear stability analysis on the go-or-grow model, we recover the same wave speed expression. In addition, we numerically explore how the key parameters influence the traveling wave speed profile. Our analysis indicated the counter-intuitive result that the wave speed is independent of the matrix degradation rate, and our simulations show that, at most, the speed is weakly dependent on this parameter.

Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each process is rarely known a priori and may be difficult to infer from data. We propose biochemically informed neural ordinary differential equations (BINODEs), a neural-ODE framework that retains the stoichiometric structure of mechanistic models while representing individual processes by neural networks. In BINODEs, the outputs of neural network processes (NNPs) are mapped to state derivatives through a linear layer analogous to a stoichiometric matrix. This architecture allows biological side information, such as process-specific inputs, sign constraints, and monotonicity assumptions, to be built directly into the model. We characterize the approximation properties of NNPs for several standard biochemical rate laws and show that the proposed framework recovers both trajectories and process-level structure in Monod, Lotka-Volterra, pharmacokinetic, and ultradian endocrine models. These results suggest that BINODEs offer a useful compromise between mechanistic interpretability and data-driven flexibility for modeling partially known biochemical or biological dynamical systems.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity. Author SummaryAlthough the mechanisms driving seasonality of respiratory disease dynamics have been well-studied in temperate regions, they are unknown in the tropics. In this study, we used a 10-year influenza-like-illness (ILI) daily-reporting data set collected from outpatient clinics in Ho Chi Minh City (HCMC) in Vietnam to investigate the mechanisms associated with annual and nonannual ([~]215 days) periodic patterns in the data. By comparing seven mechanistic models against the data, we showed that the mechanism that best explains respiratory disease dynamics in HCMC is a stochastic susceptible-infected-recovered-susceptible (SIRS) model weakly driven by external drivers including specific humidity, temperature, and school term. The nonannual cycles duration is consistent with the inferred duration of immunity of the model. By showing the nonannual cycle as strong as in the data is only observed in stochastic model, we showed that the observed respiratory disease dynamics in HCMC is under the influence of stochasticity when external drivers are weak.

The Hajj is an annual pilgrimage made by millions of Muslims to Mecca in the Kingdom of Saudi Arabia (KSA). The large number of international attendees at the Hajj increases the risk of global infectious disease spread. However, we know very little about the benefits, costs, and cost-effectiveness of testing and quarantining strategies to contain epidemic spread during mass gathering events. In this work we developed a stochastic discrete-time compartmental metapopulation model to simulate international epidemics of infectious pathogens and their potential importation into KSA during the Hajj. We used the model and an epidemic simulation study to evaluate the impact and cost-effectiveness of three testing and quarantining strategies for arriving pilgrims: randomly testing 99% of pilgrims, 80% of pilgrims, or using a symptom-based screening strategy. The simulations lasted 100 days, covering the 30 days before the Hajj and 65 days after the Hajj. Under the conditions assumed in our simulation study, there was strong evidence that testing and quarantining strategies are cost-effective measures for controlling epidemic threats at the Hajj. The median net monetary benefits of intervention strategies ranged from Intl$-41.89M [95% quantile range Intl$-42.37M to Intl$3.18B] to Intl$12.68B [Intl$-8.70B to Intl$13.82B] across scenarios with different pathogen characteristics (based on the natural histories of SARS-CoV-2 and H1N1 Influenza) and epidemic seed locations. Our results were sensitive to the data sources that were used to estimate the number of pilgrims travelling to KSA by origin country, with flight passenger statistics providing biased estimates of pilgrim numbers. Our work provides an adaptable tool to inform infectious disease risk assessments and evaluate the cost-effectiveness of possible disease control measures for the Hajj, and could be extended to other mass gathering events.

Cardiovascular disease is one of the leading causes of death worldwide, with myocardial infarction (MI) being a major cause of both morbidity and mortality among cardiovascular patients. MI Patients face a higher risk of cardiovascular disease recurrence afterwards. Therefore, accurately predicting the risk of recurrence and identifying key risk factors are crucial for clinical decision-making. In this paper, we consider the interrelationships among cardiovascular factors from a systemic perspective. We first construct a differential network for each patient to capture individual-specific deviations in factor relationships and propose a novel method, termed Causal Factor-aware Graph Neural Network (CFGNN), which integrates factor interactions to predict the recurrence risk of MI patients while uncovering key risk factors from a causal perspective. Experimental results demonstrate that CFGNN performs well on hospital-derived datasets in real world, effectively identifying several key risk factors. This method not only deepens our understanding of cardiovascular disease, but also paves the way for more targeted and effective interventions.

Mainland China experienced multiple waves of COVID-19 pandemic during 2020-2022, driven by emerging variants and changes in public health and social measures (PHSMs). We developed a hypergraph-based Susceptible-Vaccinated-Exposed-Infectious-Recovered-Susceptible (SVEIRS) model to reconstruct epidemic dynamics across 31 provinces, capturing transmission heterogeneity associated with clustered contacts. We assessed key characteristics of transmission at national and provincial levels during four outbreak periods: initial, localized pre-delta, Delta, and widespread Omicron, which accounted for 96.7% of all infections. We found significant diversity in transmission contributions across cluster sizes, with a small fraction of larger clusters responsible for a disproportionate share of infections. Counterfactual analyses showed that reducing cluster-size heterogeneity, while holding overall exposure constant, could have lowered national infections by 11.70-30.79%, with the largest effects during Omicron period. Ascertainment rates increased over time but remained spatially heterogeneous with a range: (14.40, 71.93)%. Population susceptibility declined following mass vaccination (to 42.49% in Aug 2021, nationally) and rebounded (to 89.89% in Nov 2022) due to waning immunity with variations across the provinces. Effective reproduction numbers displayed marked temporal and spatial variability, with higher estimates during Omicron. Overall, these results highlight critical role of group contact heterogeneity in shaping epidemic dynamics.

Physical activity (PA) plays an important role in maintaining and improving health. Daily steps have been a key PA measure that is easily accessible with common wearable devices. However, methods are lacking to recommend a personalized optimal distribution of daily steps over a period of time for the best of certain health biomarkers. In this paper, we fill this void based on the data from the All of Us Research Program which includes months of step counts as well as repeated measurements of key health biomarkers. We develop a new offline reinforcement learning (RL) algorithm to learn personalized and optimal PA distributions associated with cardiometabolic risk, where the action is a function representing the daily step distribution over a period of time. Simulation studies demonstrate the advantage of the proposed approach over existing continuous-action RL methods. The learned optimal policy from the All of Us data generally suggests people take more daily steps and also follow a more consistent pattern of PA over time while offering tailored recommendations for subgroups in blood glucose level, body mass index, blood pressure, age, and sex.

While nitrogen fertilizers are widely used in agricultural production, their application incurs significant environmental and energetic costs. In contrast, some crops are less dependent on these fertilizers because they engage in symbioses with rhizobia, nitrogen-fixing bacteria provide ammonium to the plant in exchange for carbon. However, the carbon cost associated with nitrogen fixation can negatively impact crop yields. Improving the efficiency of this metabolic process could alleviate this impact on crop productivity. Mathematical models can help us quantitatively explore metabolic behavior and identify potential targets for metabolic engineering. In this work, we developed a kinetic model of determinate root nodule metabolism, where this symbiotic exchange of carbon from the plant and nitrogen from the bacteria occurs. We used this model to evaluate how the predicted metabolic behavior differs between inefficient and efficient nodules, and to identify potential engineering targets for improving nitrogen fixation efficiency and rate. We show that the enzymes phosphoenolpyruvate carboxylase and pyruvate kinase have significant influence on the predicted rate and efficiency of nitrogen fixation, especially when their expression is varied in combination with oxidative Pentose Phosphate Pathway enzymes like glucose-6-phosphate dehydrogenase and 6-phosphogluconolactonase. The model predicts that pairing a 3-fold decrease in glucose-6-phosphate dehydrogenase activity along with either a 3-fold increase in phosphoenolpyruvate carboxylase activity or decrease in pyruvate kinase activity could increase nitrogen fixation rate by 5.51% while improving nitrogen fixation efficiency by 7.74%.

Embryo implantation is early and complex stage of pregnancy begins when competent blastocyst makes a physiological attachment to receptive endometrium. Expression of numerous molecules are essential for initiation of pregnancy. leukemia inhibitory factor (LIF) is essential cytokines required for priming uterus to make it receptive for implantation. In mice, the ovarian estrogen regulated expression of LIF is absolutely required for implantation. Golden hamster showed ovarian estrogen independent process of embryo implantation. Hence, the regulation of LIF in uterus of golden hamster during early pregnancy is still ambiguous. In this study, we explored the possible regulation of LIF by uterine factor and their spatio-temporal localization and expression in the uterus of golden hamster during early pregnancy and pseudopregnancy. We further demonstrated their ability to activate prostaglandin synthesizing enzymes to achieve successful pregnancy. We used immunohistochemistry, quantitative and semiquantitative PCR to achieve the objectives. We observed the expression of LIF in all the day of early pregnancy and pseudopregnancy in the uterus of hamster. Their m-RNA was found to be upregulated around the day of implantation and decidualization. LIF showed high expression in D3 pseudopregnancy. LIF was found to be regulated by estrogen in ovariectomized uterus and significantly reduced expression of LIF was observed in letrozole treated uterine horn. Downregulated expression of prostaglandin synthesizing enzymes was observed in anti-LIF antibody treated uterus. Together, these findings highlights that uterine factor regulated LIF mediate their action via activating prostaglandin synthesizing enzymes to make uterus receptive for successful early pregnancy in hamster. HighlightO_LIExpression of LIF in uterus during pregnancy in golden hamster is independent from the presence of blastocyst C_LIO_LILIF is regulated by estrogen in ovariectomized hamster C_LIO_LIExpression of LIF mRNA is downregulated in letrozole treated uterine horn in day 5 of pregnancy indicating the possibility of their regulation by uterine estrogen in golden hamster C_LIO_LIProstaglandin synthesizing enzyme and LIF might be associated with the activation of inflammatory signals which are essential for successful establishment of early pregnancy in golden hamster. C_LI

Frequent HIV testing, or "retesting," the practice of regular HIV testing following a negative test result, among persons at high risk of HIV exposure is critical for initiating treatment early among newly infected persons and reducing the risk of HIV transmission. However, barriers to HIV retesting, such as fear of stigma, underestimating risk after a prior negative HIV test, and navigating the logistics of accessing an HIV test, have contributed to lower-than-desired retesting rates in Sub-Saharan Africa, where median time from infection to diagnosis is over 2.5 years. The Innovative Behavioral Intervention Strategies (IBIS) study aims to encourage re-testing by utilizing principles of behavioral economics and human-centered-design in a many-arm randomized trial (known as a "megatrial") of avatar-delivered video-based messages and text messages to promote HIV retesting. In 2025, we conducted two-day focus groups in Kenya and Uganda to prototype the messages among community members and healthcare workers. An expert team engaged participants in various activities and discussions to elicit their feedback, where they reflected on factors such as local relevance, clarity, and visual appeal for each prototype. Key changes as a result of workshop feedback include standardized greetings for each arm, clearer language and refined translations, SMS language which protects participant privacy, and avatar updates for local acceptability, while maintaining core behavioral theory. The workshops generated important insights that shaped the final avatars, scripts, and messages encouraging HIV retesting which will be incorporated in the eventual trial. This study demonstrates the value of engaging end-users early in the intervention development process, and gives insight into the application of artificial intelligence (AI) to improve health behaviors in resource-limited settings.

This work focuses on the global and partial identification problem for fractional differential equations. We provide a general numerical procedure based on global and local optimization algorithms with two refinements for biological systems that ensure solution positivity and homogeneous parameter units. The method is applied to a new fractional model of Dengue outbreak called the Fractional Homogeneous Nishiura (FHN) model, calibrated using data of newly infected people in Cape Verde. We show that our identification method yields a better fit between data and model solutions than previous approaches and that our FHN model captures the dynamics of Dengue more closely than existing systems.