We develop a mathematical modeling framework to address the challenge in launching an effective staged vaccination campaign during a typical viral infection season to avoid an overwhelmed healthcare system for the entire season. Using the COVID-19 pandemic following its acute phase as a motivating example, our model takes into account the willingness of the public to receive vaccines, as well as the uncertainty of vaccination delivery and administration, to achieve the objective of optimizing the timing and distribution of the vaccination campaign, subject to the constraint that hospitalized cases do not exceed healthcare capacity. The integration of a dynamic transmission model with a scenario tree–based stochastic optimization framework enables the evaluation of future scenarios characterized by uncertainty in vaccination rates, contact mixing, and public adherence to safety measures. Accounting for these future scenarios facilitates the identification of strategies to dynamically adjust the timing and scale of vaccine and contact mixing during distinct phases of the viral season. Our study demonstrates that a well–timed, well–phased vaccination campaign, along with other public health interventions, can prevent overcrowding in hospitalization in a typical viral infection season.

We study a reaction-diffusion model for tick population dynamics subject to homogeneous Neumann boundary conditions and incorporating two distinct constant time delays. We introduce a Gamma-Ricker type growth function. A central analytical difficulty lies in the sublinear case, where the lack of smoothness of the nonlinearity prevents the direct application of standard regularity and stability techniques. To address this challenge, we develop a novel approach that combines model-specific differential inequality, maximum principle arguments, and dynamical systems techniques. Within this framework, we establish new criteria ensuring the global asymptotic stability of the positive steady state. Our results recover, as a special case, all known sharp stability conditions for the linear case and, more importantly, resolve a longstanding open problem for nonsmooth sublinear reproduction functions. These findings significantly advance the theoretical understanding of delayed diffusive population models with nonsmooth nonlinearities and offer new insights into the long-term behavior of tick population dynamics. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Predicting the human burden of vector-borne diseases from limited surveillance data remains a major challenge, particularly in the presence of nonlinear transmission dynamics and delayed effects arising from vector ecology and human behavior. We develop a data-driven framework based on an extension of Sparse Identification of Nonlinear Dynamics to systems with distributed memory, enabling discovery of transmission mechanisms directly from time series data. Using severe fever with thrombocytopenia syndrome as a case study, we show that this approach can uncover key features of tick-borne disease dynamics using only human incidence and local temperature data, without imposing predefined assumptions on human case reporting. We further ascertain the robustness of the recovered incidence-temperature model by integrating it with mechanistically derived tick-host covariates, showing that the forecasting ability does not improve. This suggests that the proposed core data-driven model already delivers strong predictions. The framework also allows for systematic sensitivity analysis of memory kernels and behavioral parameters. Although the approach prioritizes predictive accuracy over mechanistic transparency, it yields sparse, interpretable integral representations suitable for epidemiological forecasting. This methodology provides a scalable strategy for forecasting vector-borne disease risk and informing public health decision-making under data limitations.

We consider an integro-differential equation with spatially varying delay, motivated by the tick population dynamics with development delay influenced by spatially varying environmental conditions. We establish the threshold dynamics and show how the spatial distribution of the positive equilibrium (if exists) is impacted by the spatial heterogeneity of the development delay. Our analysis illustrates two novel phenomena for the ecological system modeled. First of all, population survival is highly sensitive to environmental change rates: slow changes cause extinction, whereas rapid changes facilitate survival through redistributing the population in space. Secondly, for a given mode of spatial distribution, we can select a corresponding spatially varying development delay so that the stable positive equilibrium has the target mode. Numerical examples are provided to further illustrate the theoretical findings and their implications for spatially relevant control measures of tick populations and relevant tick-borne diseases. (c) 2025 Published by Elsevier Inc.

Mpox is a viral zoonotic disease that has gained global attention due to its recurrent outbreaks in endemic regions of Africa and beyond. The recent clade I outbreak in the Democratic Republic of the Congo (DRC) has been characterized by extensive transmission among children - particularly those under 15 years of age—and adults with elevated occupational risks, such as healthcare workers, sex workers, and hunters. Motivated by emerging evidence that vaccination alone may not explain the observed decline in mpox transmission across the DRC, and recognizing that behavioural modification is more feasible among adults, this study investigates the synergistic impact of vaccination and behaviour-driven contact reduction among high-risk adults within an age- and risk-structured modelling framework. The model stratifies the population into adults (high- and low-risk groups) and children. It incorporates vaccination for both adults and children, as well as behavioural adaptations (in the form of contact reduction) among high-risk adults. The model is calibrated to weekly reported mpox cases in the DRC from January 2024 to April 2025, from which key parameters are estimated. Scenario analyses reveal that among the adult population, behavioural change has a greater impact than vaccination in reducing mpox transmission. The model indicated that vaccination targeting children yielded the most significant effects, in comparison to either contact-reduction measures or immunization of adults. Moreover, our results indicate that initiating a 50% reduction in contact rates among high-risk adults approximately 20 weeks earlier yields an additional 20% decrease in the cumulative number of mpox cases, compared with implementing the same reduction concurrently with the vaccination intervention in the DRC. Given the current low vaccination coverage and supply constraints, our findings provide evidence-based guidance for optimizing vaccine allocation and prioritizing behavioural interventions among high-risk groups to prevent sustained transmission.

A correlation analysis of the Gulf Coast tick (Amblyomma maculatum Koch) count data collected in 1985, 1987, and 1991 from the Shay Ranch in Refugio County Texas demonstrated host selection preference by questing females to the host cattle with feeding/fed male ticks. Here, we develop a novel mathematical model to incorporate this host selection preference, and we use this model to explore the male-female ratio of feeding ticks at the equilibrium state, and to describe the impact of the selection preference by female ticks on mating, reproduction success, and tick population dynamics. The model set-up involves the stratification of questing adult ticks by sex and mating status, and stratification of hosts infested by different categories of ticks. Our equilibrium state analysis illustrates Allee effects due to low mating probability with a small number of ticks distributed over a large number of hosts, where the infestation-free equilibrium is always asymptotically stable. We also give conditions for the existence of infestation-establishment equilibria, in terms of the maximum number of eggs reproduced and survived during the tick life cycle, the adult tick questing rate, and the host selection preference. The model set-up and the established male-female ratio at the equilibrium state provide insight into tactics for tick population suppression strategies. This study also suggests many topics for future studies on a system of delay differential equations with complex nonlinearities due to host selection preference.

Social distancing was a cornerstone of the COVID-19 pandemic response, yet evidence on factors associated with adherence remains fragmented and context-specific. We conducted a global meta-analysis to quantify the associations between key individual-level determinants and adherence to social distancing measures. We systematically searched six electronic databases from inception to August 20, 2025 to identify studies reporting associations between individual-level determinants and adherence to social distancing measures. Effect estimates were transformed into Pearson’s correlation coefficients (r) and pooled using random-effects meta-analysis. Subgroup analyses and meta-regression were conducted to examine regional and temporal variation. Of 10,804 records identified, 58 cross‑sectional studies comprising 545,640 participants were included, and fourteen determinants of adherence to social distancing were assessed. Higher educational attainment (r = 0.09), female sex (r = 0.08), being married (r = 0.08), older age (r = 0.06), higher income (r = 0.07), and greater perceived risk and severity of COVID-19 (r = 0.10) were positively associated with adherence, whereas more conservative political ideology was negatively associated (r = –0.12). No significant associations were observed for perceived government response, comorbidity, place of residence, knowledge and awareness, smoking, employment status, or essential worker status. The magnitude and statistical significance of several associations varied across World Health Organization regions, with the European region showing the highest number of determinants significantly associated with adherence, whereas the African and Eastern Mediterranean regions exhibited the fewest. Adherence to social distancing during COVID-19 was associated with a set of demographic, socioeconomic, psychological, and political factors, with substantial regional heterogeneity. These findings underscore the importance of accounting for contextual and structural differences when interpreting behavioural evidence and designing public health responses to future disease outbreaks.

We develop and calibrate a two-layer macroeconomic model of a pandemic to examine the macroeconomic costs and benefits of COVID-19 public health interventions. By integrating policies into a stratified epidemic compartmental model (Susceptible-Infected-Recovered, or SIR), we analyze the impact of non-pharmaceutical interventions (NPIs) on disease transmission. We then apply a dynamic stochastic general equilibrium (DSGE) model to simulate the effects of containment policy shocks on consumption, labor supply, and production, and their implications for macroeconomic variables. The model is calibrated and simulated for the province of Ontario, Canada. Our findings highlight the significant reduction in infections due to NPIs, quantify the negative economic consequences of policy shocks, and acknowledge that labor market flexibility and business adaptations played a key role in mitigating these adverse effects. This study provides a qualitative framework for evaluating the delicate balance between public health and economic considerations in policymaking during a public health emergency.

Urban transit systems, particularly those in major metropolitan areas, are becoming increasingly interconnected, making it essential to better understand passenger mobility and its implications for the spread of infectious diseases. Respiratory infectious diseases, including COVID-19 (as a case study), can spread rapidly in densely populated urban environments, particularly within public transportation systems. This study investigates the dynamics of infection spread at a subway station, and its surrounding community, focusing on both short-term and long-term transmission. Using two deterministic ordinary differential equation (ODE) models, we simulate disease transmission over a single business day and examine how daily encounters impact infection numbers over the subsequent three months. The short-term model captures localized interactions between transit passengers and community residents, while the long-term model evaluates the cumulative impact of these encounters on community infections. Parameter estimation was performed using ridership data and the least squares method. Results suggest that mobility-related factors, particularly inflow and outflow rates, have a greater impact on controlling disease spread than transmission rates in both short- and long-term dynamics. Reducing inflow eases congestion and lowers encounters in the hub but increases encounters in the community, whereas reducing outflow increases crowding in the hub while decreasing encounters in the community. Joint reductions in inflow and outflow decrease encounters in both settings. In the long term, changes in transmission rates have only a limited effect on peak infections, while reducing outflow notably decreases infections and reducing inflow slightly increases community infections. Overall, simultaneously reducing inflow and outflow is the most effective strategy for limiting encounters in the short term and infections in the long term.

Rebound, arising from an increase in viral load after initial treatment to levels sufficient for renewed infectiousness, has been observed in COVID-19 patients, prompting concerns about patient outcomes and potential implications for transmission and disease control. To assess the impact of viral rebound on post-treatment transmission dynamics, we developed a delay differential model parameterised with characteristics of SARS-CoV-2 infection and the rebound risk observed during treatment with Paxlovid. The model explicitly accounts for the timing of treatment initiation relative to symptom onset and the duration of treatment. By varying the relative transmissibility of individuals experiencing rebound, our simulations show that rebound events comprise only a small proportion of treated cases when treatment initiation is delayed after symptom onset or when treatment duration is extended beyond the standard five-day course. However, as the proportion of symptomatic individuals receiving treatment increases, the transmissibility of rebound infections becomes a dominant factor in disease spread. A short, five-day treatment course can amplify rebound-associated transmission and substantially increase total infections when rebound transmissibility is high. In contrast, extending treatment duration from five to eight days markedly reduces the contribution of rebound cases to overall spread. Both delayed initiation and extended treatment duration decrease the risk of viral rebound, underscoring a trade-off between reducing acute transmission and mitigating post-treatment resurgence. These findings highlight the importance of integrating rebound risk into antiviral deployment strategies to improve patient outcomes and enhance population-level disease control.

We develop and analyze a mosquito population suppression delay model that incorporates survival probability during the maturation process. The model allows the trivial equilibrium to coexist with two positive equilibria and exhibits steady-state behavior including asymptotic stability, semi-stability and bistability. We analyze the subsets of basins of attraction for each stable equilibrium. Using delay as a bifurcation parameter, we examine the onset and global continuation of Hopf bifurcating periodic solutions by the global Hopf bifurcation theorem and the Bendixson criterion. Finally, some numerical examples are provided to validate the theoretical findings.

We develop a theory of invariant manifolds for phase-field system on some high-dimensional domains. The phase-field system is a generalized model describing the statics and dynamics of an interface between two phases of specific materials within the framework of Landau-Ginzburg theory. The underlying feature of the problem under consideration is the intrinsic hyperbolic nature. We prove the existence of a finite-dimensional Lipschitz manifold in the possible absence of the spectral gap condition. The manifold, which has a certain regularity, is locally forward invariant. Its basin of exponential attraction is a proper subspace of the phase space. Moreover, we prove that the manifold contains a global attractor with additional technical assumptions on the nonlinearities, which implies in particular that the basin of attraction coincides with the whole phase space. The manifold gives a geometric insight into the long-term asymptotic behaviors from the perspective of finite-dimensional reduction. (c) 2026 Elsevier Masson SAS. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

AbstractMathematical models have produced important insights into the relationships between disease transmission, risk perception, and human behaviour. However, the increase in scale and complexity of health and behavioural data accelerated by the COVID-19 pandemic demands a critical evaluation of the realism and readiness of mathematical models of infectious disease dynamics to inform preparation and response to (re)emerging public health threats. In this scoping review, we identify five thematic frontiers in extending coupled models of disease dynamics and human behaviour, spanning (1) information quality and scale, (2) data-driven versus perceived risk, (3) social influence, (4) barriers related to fatigue and access, and (5) disruptive events. For each frontier, we summarize key modelling approaches and results, identify knowledge gaps and provide recommendations on future directions with a focus on integrating big data into epidemiological models, incorporating social behavioural theory and accounting for heterogeneity within populations. In turn, each of these frontiers involves challenges that call for new analytical and technical developments. We close by providing general recommendations for modelers with a focus on interdisciplinary collaboration with social and behavioural scientists and establishing best practices for data collection and management to improve the public health relevance of infectious disease models.

Chlamydia trachomatis (CT) remains the most reported bacterial sexually transmitted infection in the United States (US), underscoring the urgent need for an effective vaccine. An agent-based model calibrated to the US National Survey of Family Growth (NSFG) and National Health and Nutrition Examination Survey (NHANES) datasets was developed and used to study the impact of vaccine on the CT and all-cause pelvic inflammatory disease (PID) burden. The model was further validated against independent epidemiological data. Here we show that a conventional vaccine with 50% efficacy and 60% coverage can achieve a 64.2% [95%CI: 43.0-68.1] reduction in chlamydia prevalence and a 14.3% [95%CI: 10.1-29.4] reduction in the prevalence of women with one or more lifetime episodes of all-cause PID. Prioritizing vaccination among individuals aged 15-24 yielded the greatest impact, even with moderate vaccine performance, highlighting the importance of age-targeted, gender-inclusive strategies. These findings provide quantitative evidence to support the design and implementation of chlamydia vaccination programs and highlight the value of agent-based modeling frameworks for evaluating complex intervention strategies in sexually transmitted infections.

We study a pulse-switching planar system that arises from describing the population dynamics of wild mosquitoes under the pulse-switching releases of Wolbachia-infected males. The periodic pulse switching between two systems renders the traditional qualitative method of planar systems ineffective. We develop a geometric approach to determine the maximal invariant set and the fixed points of the associated Poincare'\ map. This enables us to describe scenarios of global dynamics---extinction and bistability---in the sense of an extinction equilibrium coexisting with a periodic solution with a large amplitude and to locate the periodic solutions. Examples will be given to illustrate how our theoretical results can be used to inform the optimal design of pulse-releasing strategies.

The migration of nonpoint source (NPS) pollution is influenced by the resistance cost distance between landscape units and rivers. Understanding the relationship between landscape proximity and riverine pollutants is crucial for optimizing landscape patterns to mitigate NPS pollution. However, given that water quality responses to landscape patterns may depend on the proximity of landscape units to rivers and exhibit nonlinear tendencies, these relationships remain poorly understood. This study applied redundancy analysis and nonlinear segmented regression analysis to evaluate the effects of landscape patterns on NPS pollution migration in a headwater watershed in eastern China, comprising 29 sub-watersheds with diverse landscape characteristics. The results revealed that landscape patterns in the high-proximity zone were most effective in explaining riverine pollutant variations during the wet season, while those in the extremely low-proximity zone were more influential during the dry season. Therefore, landscape pattern regulation should adopt a multiscale perspective. The key landscape indicators affecting water quality differed across proximity zones. In the high-proximity zone, the land-use intensity index (LI), percentage of residential area (Res), and aggregation index of residential areas (AI_res) were crucial. In the extremely low-proximity zone, LI and the aggregation index of forestland (AI_for) played dominant roles. To improve water quality, landscape planning should consider maintaining LI < 183.22 and AI_res < 92.66 % in the high-proximity zone, and AI_for < 95.68 % in the extremely low-proximity zone. This study highlights that optimizing landscape patterns through a multiscale approach and the consideration of landscape thresholds could enhance the effectiveness of NPS pollution control and ultimately improve water quality in headwater watersheds.

BackgroundYellow Fever (YF), a disease typically transmitted to humans by infected mosquitoes, is endemic to regions such as South America. Climate change plays a crucial role in exacerbating the spread of YF.ModelWe formulate a mathematical model of YF transmission with a case study of the region in the southeastern Brazil with a well documented 2017/2018 outbreak. We validate the model using historical data, then run simulations to generate projections of future outbreaks under different climate scenarios in 2050. We also evaluate the outcomes of different mitigation measures such as emergency vaccination programs.FindingsOur results suggest that under all projected climate scenarios, increasing temperatures will yield a marked increase in the total number of cases. Under RCP 8.5, the basic human infection reproduction number will increase by 11.4%, and the cumulative infections will increase by 8.1%. The model predicts a similar increase under a moderate radiative forcing scenario. The introduction of additional emergency vaccination, at a rate of 8.0% (equivalent to 60% vaccination coverage over the course of 15 weeks) of the susceptible population per week, can reduce this increase of cumulative cases to approximately 4.9%. This effect of emergency vaccines will be equivalent to alternative public health interventions to reduce the mosquito-to-human disease transmission effective contact by approximately 23.0%. Increasing temperatures and rainfall due to climate change are projected to increase YF cases. Vaccination can be an important part of integrative mitigating measures.

We considered a model for an infectious disease outbreak, when the depletion of susceptible individuals is negligible, and assumed that individuals adapt their behavior according to the information they receive about new cases. In line with the information index approach, we supposed that individuals react to past information according to a memory kernel that is continuously distributed in the past. We analyzed equilibria and their stability, with analytical results for selected cases. Thanks to the recently developed pseudospectral approximation of delay equations, we studied numerically the long-term dynamics of the model for memory kernels defined by gamma distributions with a general non-integer shape parameter, extending the analysis beyond what is allowed by the linear chain trick. In agreement with previous studies, we showed that behavior adaptation alone can cause sustained waves of infections even in an outbreak scenario, and notably in the absence of other processes like demographic turnover, seasonality, or waning immunity. Our analysis gives a more general insight into how the period and peak of epidemic waves depend on the shape of the memory kernel and how the level of minimal contact impacts the stability of the behavior-induced positive equilibrium.