Search Results (141)

Background: Epidemic meningococcal meningitis in the African meningitis belt recurs on two timescales: a sharp annual dry-season peak and irregular multi-annual epidemics five to twelve years apart, whose mechanistic origin remains unsettled. Invasive disease is a rare, dead-end outcome of asymptomatic nasopharyngeal carriage, so susceptible–infectious templates misrepresent community transmission. We ask how carriage structure shapes bifurcation, seasonal recurrence, and the reach of conjugate-vaccine strategies. Methods: We formulate a deterministic carriage-structured model in which only carriers transmit, immunity against re-acquisition is leaky, and a conjugate vaccine is imperfect and wanes. We use the Castillo-Chavez–Song centre manifold method, numerical continuation, Floquet and eigenvalue analysis, and scenario simulations of abstract rate- and pulse-type interventions parameterised from published belt ranges. Results: The basic reproduction number ${\mathcal{R}}_0$ is a property of carriage transmission, decoupled to first order from disease incidence. Backward bifurcation at ${\mathcal{R}}_0=1$ is governed by a threshold ${\epsilon }^{\ast }$ on carriage-blocking immunity; only the untreated fatality hazard and treatment capacity are absent from the local condition. It is impossible without vaccination and, with any positive routine coverage, persists across the plausible coverage range, giving vaccine-induced bistability. Continuation confirms a fold at ${\mathcal{R}}_{0,c}\approx 0.946$ ($\phi =0.12{\mathrm{yr}}^{-1}$, weak carriage immunity), but not at baseline immunity. Under seasonal forcing, dynamics converge to a simple annual cycle throughout the region searched; we found no multi-annual recurrence, although damped eigenmodes of the unforced system have periods overlapping the observed interval. Conclusions: Within this deterministic, single-strain model, irregular recurrence likely requires additional structure, with stochastic amplification of damped cycles a natural next step. Whether sustained immunisation eliminates epidemics or merely postpones them may depend on the same carriage-efficacy threshold that governs the bistability result. Full article

African swine fever (ASF) remains a major challenge for veterinary surveillance because of its complex spatial spread across neighbouring regions. We present a Bayesian susceptible–infected–susceptible (SIS) model on a graph in which European NUTS2 regions are the nodes and transmission from a reported region j to a susceptible region i decays with geographic distance between their centroids, with strength $p_{j\to i}\propto d_{ji}^{-{\alpha }_1}$ and a small spontaneous-infection term. Transitions to a state with no reported ASF outbreaks are modelled using a logit-link function that combines regional case counts with continuing infection pressure from nearby infected regions. Bayesian inference is performed using stochastic variational inference (VI) and validated against Hamiltonian Monte Carlo using the No-U-Turn Sampler (NUTS). The model was evaluated on twelve hold-out months and compared with a persistence baseline. The proposed model achieved a lower overall log-loss than the persistence baseline (0.099 for VI and 0.095 for MCMC versus 0.127), with the largest gains on newly infected regions (information gain of +2.51 nats for VI and +2.65 nats for MCMC relative to persistence). VI and MCMC produced nearly identical predictive performance (average precision 0.895 versus 0.894), indicating that the mean-field variational approximation reliably captures the posterior predictive distribution for this model despite overdispersed marginal posteriors. For early warning of emerging outbreaks, flagging the ten highest-risk previously clear regions each month would have identified 36–38% of the 53 new outbreaks in the hold-out period, compared with none under the persistence baseline. The proposed framework provides an interpretable Bayesian model for regional ASF surveillance, demonstrating that distance-weighted graph-based epidemic models can improve early detection of emerging outbreaks. Full article

Modeling diabetic illness with random perturbations is the goal of this work. The proposed model consists of three classes: the pre-diabetic population, the diabetic population with complications, and the diabetic population without complications. We examined the suggested problem to determine at least one unique solution within the positive feasible region. The stationary distribution of this model was also explored, and the non-negative $C^2$-Lyapunov function was used to create an adequate condition for the persistence of one stationary ergodic distribution. For this model, the existence and uniqueness of the solution were also established. Additionally, the stochastic non-standard finite difference (NSFD) scheme was developed for the model. The consistency and stability of the scheme were analyzed, showing that it is consistent and stable in the mean-square sense. The underlying system admits a unique endemic equilibrium point. Finally, a test problem was studied by using a numerical technique, varying the noise levels, and maintaining the same parameter values. The outcomes for each stated class were numerically simulated in order to validate our proposed approach. Full article

Measles virus infection couples nonlinear processes across biological scales, including within-host viral amplification, immune-cell depletion, delayed adaptive control, persistent viral RNA, heterogeneous host severity and vaccination-dependent population spread. A multiscale mathematical framework is developed by coupling a seven-variable within-host ordinary differential equation model to a stochastic cellular automaton. The within-host system extends a four-variable measles immunodynamics core by including IFN-$\gamma$-dominant and IL-17-associated immune responses, persistent viral RNA and neutralizing antibodies. Six host archetypes are represented as structured parameter perturbations of this common dynamical core. The principal novelty is an explicit cross-scale coupling operator that separates genuinely ODE-derived host descriptors from hybrid epidemiological mapping rules and independently specified population-level contact and susceptibility assumptions, allowing within-host heterogeneity to propagate transparently into a spatial stochastic epidemic model. An explicit ODE-to-cellular-automaton map translates within-host trajectories into infectious timing, daily infectivity profiles and an illustrative ODE-informed severity-to-death transition mapping used internally by the cellular automaton. The mortality map depends on viral burden, infectious duration, IFN-$\gamma$ deficit, cumulative infectivity and an immune-deficit–infectivity interaction term. Population simulations show a nonlinear reduction in attack rate with increasing vaccination coverage, reduced modeled death burden under targeted high-risk in silico perturbations and additional suppression under reactive vaccination campaigns. A direct local cellular-automaton secondary-infection estimate is reported instead of interpreting cumulative infectivity burden as a reproduction number. A targeted contact-structure sensitivity further shows that matching the expected local direct-secondary-infection potential does not imply equivalent population-level attack rates, emphasizing that the quantitative CA outcomes are geometry specific. Sobol sensitivity analysis with convergence up to $N_{\mathrm{base}}=4096$ identifies core viral and immune parameters as dominant drivers of within-host and multiscale outputs. The framework provides an explicit dynamical-systems approach for coupling differential-equation immunodynamics to spatial stochastic population models in mathematical biology. Full article

Outpatient care facilities combine high patient turnover, repeated short contacts, accompanying persons, clinically vulnerable subgroups, and healthcare-worker movement across functional zones. This study develops a synthetic dynamic contact-network simulation framework to evaluate how outpatient flow-control strategies affect simulated respiratory-infection risk and service efficiency. Public descriptions of the SocioPatterns hospital-ward study were used only to shape role composition and qualitative contact heterogeneity. A parameterized outpatient process model generated time-stamped locations for patients, accompanying persons, high-risk patients, and healthcare workers over a simulated clinic day. Zone- and role-dependent temporal contacts were then coupled to a stochastic SEIR process, with 500 replications per main scenario. In the baseline scenario, mean cumulative secondary infections were 0.502 per clinic day, the probability of at least one secondary infection was 0.354, and mean waiting time was 23.1 min. Time-spaced appointments reduced mean secondary infections by 45.4–52.2% while also reducing waiting time. Accompaniment restriction reduced risk by removing non-service nodes, whereas waiting-capacity control, protected scheduling, and healthcare-worker grouping were more context dependent. The strongest combined strategy reduced mean secondary infections by 52.6% and maintained a mean waiting time of 13.6 min. These results are comparative outputs under stated assumptions, not predictions for a specific clinic. The framework provides a reproducible computational basis for testing how operational policies reshape temporal contact opportunities before local implementation. Full article

Urban transmission of dengue and other Aedes aegypti-borne diseases is shaped by the interaction of vector ecology, human mobility, climate, and spatial heterogeneity. Capturing these interactions in city-specific settings requires models that are detailed enough to represent local transmission processes, while remaining computationally feasible for calibration, validation, and sensitivity analysis. This study presents a hybrid agent-based modeling and simulation (HABMS) approach, supported by high-performance computing (HPC), for simulating urban vector-borne disease transmission. Human residents are represented as mobile agents with stochastic infection dynamics, while mosquito populations are represented at the patch level through discrete-time equations. The model incorporates geospatial structure, temperature, land-use-based human movement, and local contextual information to represent transmission within urban environments. The framework was applied to Santa Marta, Colombia, as a city-specific case study. Transmission parameters were calibrated using surrogate-based Bayesian optimization, and their influence was assessed through sensitivity analysis. High-performance computing made the large number of stochastic simulations required for calibration and sensitivity analysis feasible. The calibrated model reproduced the magnitude and main seasonal shape of the observed dengue epidemic, including the peak and early decline. However, the model did not fully reproduce the late low-incidence tail of the season, indicating the need to incorporate external introductions of infection and rainfall-driven seasonal forcing of vector recruitment in future versions. A control scenario run on the calibrated baseline, a 30% reduction in larval carrying capacity, lowered the simulated seasonal attack rate by about three quarters and moved the system below the threshold at which local transmission is self-sustaining, illustrating the relative comparisons the calibrated model supports. This study contributes an adaptable hybrid model architecture and a high-performance implementation that make city-specific calibration and sensitivity analysis computationally feasible, demonstrated through a case study in Santa Marta. Full article

This paper proposes a novel susceptible–infected–susceptible (SIS) epidemic model incorporating a fractional-order term and white-noise perturbations. Several analytical results concerning its dynamical behavior are established. Firstly, we prove the existence and uniqueness of model solutions using the Carathéodory approximation. Secondly, the extinction of disease is rigorously proven based on the properties of the quadratic function. Meanwhile, the Ulam–Hyers stability of the model is derived by using stochastic Gronwall-type inequalities and the stochastic analysis techniques. Furthermore, the solution of the proposed fractional-order stochastic model can be approximated by that of the corresponding averaged model under suitable averaging conditions. Then, numerical simulations are conducted to illustrate the effects of key parameters on disease extinction, stability, and long-term dynamical behavior. To improve its adaptability to real-world epidemic dynamics, this paper embeds dynamical constraints into neural networks and constructs a stochastic physics-informed identification framework for seasonal infectious diseases. Empirical results based on monthly influenza data from Xinjiang show that the proposed framework can capture epidemic trends, seasonal peaks, and fitting uncertainty. These results provide a theoretically grounded and practically applicable approach for infectious disease modeling under memory effects and stochastic perturbations. Full article

In-depth analysis of epidemic models, particularly for cholera, is crucial because they serve as significant tools for disease transmission prediction, evaluation of control strategies, and optimization of healthcare resource management. The stochastic models provide increased realism by incorporating environmental uncertainty such as variability in water quality, disparities in access to sanitation, and population mobility. The present work generalizes a deterministic two-patch cholera model to a stochastic framework. We first prove the existence and uniqueness of global solutions, then establish the extinction condition $R_0^{*}<1$ for disease eradication in the long term. A key contribution lies in proving the existence of a unique ergodic stationary distribution when $R_0^{\left(1\right)}>1$ and $R_0^{\left(2\right)}>1$. Furthermore, we derive the stochastic threshold $R_0=\text{max}\{R_0^{\left(1\right)},R_0^{\left(2\right)}\}$, which corresponds to the basic reproduction number ${\mathcal{R}}_0=\text{max}\{{\mathcal{R}}_0^{\left(1\right)},{\mathcal{R}}_0^{\left(2\right)}\}$. Lastly, numerical simulations are employed to confirm theoretical results. Full article

East Coast Fever (ECF) causes approximately one million livestock deaths annually in sub-Saharan Africa, posing a significant threat to livestock. The wildlife–livestock interface complicates disease management, as wildlife serve as reservoirs. This study developed a Continuous Time Markov Chain (CTMC) model incorporating the wildlife–livestock interface to analyze ECF dynamics. Using the Galton–Watson approximation, we assessed the probability of disease extinction following the introduction of infected hosts or vectors. The probability of disease extinction calculated from the branching process is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of the deterministic model and the CTMC model are compared to ascertain the effect of demographic stochasticity on ECF dynamics. Differences in model predictions and asymptotic dynamics between stochastic and deterministic models were evident. The deterministic and stochastic formulations should therefore be viewed as complementary modeling frameworks, with the deterministic model characterizing average epidemic dynamics and the CTMC model capturing the probabilistic variability and extinction behavior inherent in real transmission processes. These differences are crucial for intervention strategies earmarked to prevent outbreaks. Our analysis revealed a high probability of ECF extinction if the disease emerges from recovered carrier cattle. Finite time to ECF disease extinction is estimated using 10,000 sample paths, and it is shown that the epidemic duration is shortest if the disease is introduced by infectious cattle. The epidemic duration is longest when the disease is introduced by infectious ticks. Additionally, we observed that host interactions at the wildlife–livestock interface play a critical role in shaping ECF transmission and informing control strategies. Full article

Influence Maximization (IM) is a fundamental problem in social network analysis that aims to identify a set of k seed nodes that maximizes influence spread under a given propagation model. Despite its importance in applications such as viral marketing and epidemic control, the IM problem is NP-hard, making exact solutions computationally infeasible for large-scale networks. Existing approximation methods typically rely either on static centrality heuristics, which often ignore global network structure, or on metaheuristic algorithms, which may suffer from slow convergence due to random initialization. This paper proposes a novel approach, termed Advanced Centrality-Driven Discrete Particle Swarm Optimization (DPSO), which integrates a weighted hybrid centrality score combining Degree, PageRank, and Betweenness centrality to guide the stochastic search process. In addition, a systematic grid search methodology is employed to determine the optimal weight configuration of the hybrid score. Experiments conducted on three real-world datasets (Twitter, ego-Facebook, and ca-HepTh) demonstrate that the optimal seeding strategy is strongly dependent on network topology. The results show that dense social networks favor popularity-based metrics such as Degree and PageRank, whereas sparse collaboration networks benefit significantly from bridge-oriented metrics such as Betweenness centrality. Overall, the proposed method achieves consistent improvements in influence spread across different network types, with the largest gains (up to 70%) observed in sparse network settings. Full article

Viral and fungal diseases of greenhouse strawberries lead to significant crop losses, while traditional uniform spraying schemes do not account for the actual distribution of infection foci or changes in the microclimate. This paper proposes an integrated system for greenhouse farms that combines a stochastic SIRS model of the epidemic process with a microclimate-dependent infection coefficient β_eff(t), a computer vision module based on a lightweight YOLOv10n detector, and a mobile sprayer robot. For three sets of parameters corresponding to moderate infection, outbreak, and suppression scenarios, ensemble simulations are performed (100 realizations per scenario). The results show that the maximum number of infected plants reaches approximately 690 out of 1000 in the outbreak scenario and only about 28 out of 1000 in the suppression scenario, reflecting the effect of timely microclimate correction and local spraying. The YOLOv10n detector is used as a sensor to determine the proportion of affected plants I(0)/N and provides automatic formation of the initial conditions of the population model. The resulting forecasts then serve as the basis for selecting one of three operating modes for the spraying robot (observation, microclimate correction, local treatment). Unlike existing works that consider disease detection, epidemiological models, or robotic spraying separately, this paper proposes a unified closed-loop scheme of “computer vision—stochastic model—mobile robot,” linking detection quality with epidemic process forecasting and treatment strategy. In this study, the feasibility of the proposed system was examined through numerical simulations, detector-level performance evaluation, and offline image-based integrated validation of the detector-to-decision workflow. Full closed-loop experiments in a real greenhouse environment are planned for future work. Full article

Branching processes are stochastic models describing the evolution of populations in which individuals reproduce and die independently over time. In the classical setting, an individual’s reproductive capacity is fixed throughout its lifetime. However, in real-world situations, fertility typically rises during a juvenile phase, peaks at maturity, and subsequently declines. In order to capture this feature, we introduce a branching random walk with ageing, as an extension of the classical branching random walk, by assigning each individual an age-dependent reproductive rate. Our model differs from classical age-dependent processes such as the Bellman–Harris model, where the remaining lifespan depends on age, while the rate of reproduction is fixed within that lifetime. As in the classical case, branching random walks with ageing are parametrised by $\lambda >0$, which tunes the reproductive speed and may be seen as a characteristic of the population. The thresholds of $\lambda$ separating extinction and survival are the global and local critical parameters. We characterise the value of the local critical parameter and provide a lower bound for the global critical parameter. We identify a class of ageing branching random walks for which this lower bound coincides with the global critical parameter. We study how local modifications to the reproduction and ageing rates may change the critical parameters. This is of practical interest: in species preservation, one may want to lower the critical parameters, so that $\lambda$ exceeds them, and there is a positive probability of survival. On the other hand, in epidemic control, the goal is to increase the critical parameters, since if $\lambda$ is below them, then the epidemic is eventually going to disappear. We compute the expected number of individuals alive in a branching process with ageing and show that, contrary to the behaviour of classical branching processes, it may exhibit an initial growth even when the population is ultimately destined for extinction. Full article

The spread of Xylella fastidiosa, a xylem-limited bacterial pathogen, has caused widespread mortality among olive trees in Apulian region, Italy in more than a decade, and represents a significant threat to Mediterranean agroecosystems. To encourage evidence-based containment strategies, we developed a stochastic, spatiotemporal simulation model that represents pathogen transmission at the individual-tree level. This work integrates high-resolution georeferenced olive-tree data and implicitly incorporates vector population dynamics through a tree-specific vulnerability index, which considers local host density and landscape connectivity. Vector dispersal is approximated using a radial transmission kernel, which preserves host–vector spatial interactions while avoiding the explicit modeling of insect trajectories. The system’s spatial structure is additionally formulated as a proximity graph, facilitating network-based analysis of spread pathways. A series of Monte Carlo simulation experiments is employed for calibration against the observed epidemic footprint, while validation utilizes independent infection records and global sensitivity analysis of key parameters. The findings indicate that the model effectively replicates realistic propagation patterns, and its calibrated parameters are consistent with out-of-sample data. This makes it an appropriate exploratory tool for scenario testing, assessing the potential impact of intervention strategies, and offering risk-based decision support for handling Xylella fastidiosa outbreaks. Subsequently, graph centrality metrics are used to identify epidemiologically critical trees that function as transmission bridges, thus representing priority targets for surveillance or removal efforts. Thus, multiple tests have been conducted using betweenness and closeness centrality, while comparing both methods leads to effective node-tree removal decisions. Full article

We study a variety of stochastic contact processes—directly related to models of rumor and disease spreading—from the viewpoint of their constants of motion, either exact or approximated. As in deterministic systems, constants of motion in stochastic dynamics make it possible to reduce the number of relevant variables, thereby confining the set of accessible states and facilitating analytical treatment. For processes of rumor propagation based on the Maki–Thompson model, we show how to construct exact constants of motion as linear combinations of conserved quantities in each elementary contact event, and how they relate to the constants of motion of the corresponding mean-field equations, which are obtained as the continuous-time, large-size limit of the stochastic process. For SIR epidemic models, both in homogeneous systems and on heterogeneous networks, we find that a similar procedure produces approximate constants of motion, whose average value is preserved along the evolution. We also give examples of exact and approximate constants of motion built as nonlinear combinations of the relevant variables, whose expressions are suggested by their mean-field counterparts. Full article

As a fundamental mathematical model for complex systems, complex networks describe interactions among social, infrastructural, and biological systems. However, the complete connection structure is often unobservable, making topology reconstruction from limited data—such as time series of unit states—a crucial challenge. To address network reconstruction under sparse local observations, this paper proposes a novel framework that integrates epidemic dynamics with Dempster–Shafer (DS) evidence theory. The core of our method lies in a two-level belief fusion process: (1) Intra-node fusion, which aggregates multiple independent SIR simulation results from a single seed node to generate robust local evidence represented as Basic Probability Assignments (BPAs), effectively quantifying uncertainty; (2) Inter-node fusion, which orthogonally combines BPAs from multiple seed nodes using DS theory to synthesize a globally consistent network topology. This dual-fusion design enables the framework to handle uncertainty and conflict inherent in sparse, stochastic observations. Extensive experiments demonstrate the effectiveness and robustness of the proposed approach. It achieves stable and high reconstruction accuracy on both a synthetic 16-node benchmark network and the real-world Zachary’s Karate Club network. Furthermore, the method scales successfully to four large-scale real-world networks, attaining an average accuracy of 0.85, thereby confirming its practical applicability across networks of different scales and densities. Full article