Search Results (613)

Aggregated epidemics, characterized by rapid transmission over short periods, pose severe threats to public health security, necessitating the development of precise source tracing and simulation methods to support efficient prevention and control. However, existing studies suffer from three major gaps: (1) predominant focus on national/regional scales with limited urban-scale analysis; (2) reliance on proprietary mobile data that are often inaccessible; and (3) NP-hard computational complexity in traditional source tracing methods. To bridge these gaps, this paper proposes an integrated spatiotemporal diffusion model comprising two core components: outbreak point estimation and spatial diffusion simulation. The model first uses the SEAIR infectious disease dynamics model to predict trends, combines the 3-Sigma criterion and viral incubation period to screen early epidemiological survey data, employs a road network-constrained DBSCAN algorithm for spatial clustering, and locates the outbreak point via an improved inverse distance weighting method incorporating time and POI density weights. Subsequently, using the estimated outbreak point as the initial transmission center, and based on the “cell-type” living structure hypothesis of populations, it fuses multi-source geographic data to quantify regional attractiveness and simulate viral diffusion in grid space. The model is validated using COVID-19 epidemic data from Xi’an, Shanghai, and the Hong Kong Special Administrative Region of China. Results show that the proposed outbreak point estimation method effectively estimates the initial transmission center, with distances between estimated points and officially announced points of 0.786 km, 1.676 km, and 5.441 km, respectively—shortened by 179 m, 1091 m, and 711 m compared to related studies. The spatiotemporal diffusion model effectively simulates daily incidence patterns, achieving average coverage rates of 67.32% and 72.9% and average precision rates of 60.67% and 78.84% in Shanghai and Hong Kong, respectively, with significantly better simulation accuracy than traditional methods in the early and middle stages of the epidemic. This study provides a scientifically robust, data-parsimonious framework for precise source tracing, early warning, and resource allocation in urban epidemics, with strong generalizability to other resource-limited settings. Full article

Communities in Miami face persistent disparities in HIV prevention, including low uptake of pre-exposure prophylaxis (PrEP) and gaps in routine HIV testing. These inequities are shaped by co-occurring structural conditions, such as food insecurity, housing instability, discrimination, transportation barriers, and broader barriers to care. Understanding how these conditions interconnect may inform approaches to sustained engagement in HIV prevention. We examined how structural and sociodemographic conditions and food insecurity were interconnected and reflective of overall structural vulnerability. We conducted a cross-sectional network analysis using data from 2755 surveys collected during Phases 1 and 2 of the Five Point Initiative (FPI), a community-engaged, place-based sexual health implementation strategy in Miami. Partial correlation networks were estimated using the EBICglasso algorithm across key structural barriers to HIV prevention. We calculated network centrality metrics (strength, betweenness, closeness) to characterize the relative connectivity and positioning of conditions within the network. Secondarily, we used traditional mixed correlations to characterize bivariate associations among structural and sociodemographic factors. Multiple regression also examined associations of barriers to care, discrimination, ethnicity, education, housing instability, and income with food insecurity. Additional models examined whether these differed by race. Food insecurity emerged as having the highest strength, closeness, and betweenness centrality within the network and showed the strongest association with barriers to care. Greater food insecurity was also associated with higher discrimination, lower income, unstable housing, and Latino ethnicity. Additional significant connections among variables were also found. Similarly, in secondary bivariate analyses, food insecurity was positively correlated with barriers to care (r = 0.331), discrimination (r = 0.251), ethnicity (r = 0.141), and housing instability (r = 0.125), and negatively correlated with income (r = −0.150) and education (r = −0.079). The multivariable regression model predicting food insecurity was statistically significant, F(6, 2612) = 65.8, p < 0.001, with association directions generally consistent with the network findings. Race did not significantly moderate most individual associations with food insecurity. Race by housing interaction was significant (p = 0.03), indicating that participants who identified as Black or African American with insecure housing were more likely to experience food insecurity. Overall, the findings indicate that food insecurity occupies a prominent position within an interconnected system of social and structural constraints around HIV prevention. Structural barriers to HIV prevention operate as a mutually reinforcing system rather than isolated challenges. Addressing highly connected constraints, particularly food insecurity, housing instability, and barriers to care, through place-based, community-engaged strategies may yield compounded benefits across the prevention continuum. These findings highlight potential priorities for structural intervention in Ending the HIV Epidemic (EHE) priority jurisdictions. Full article

The global obesity epidemic underscores the urgent need to dissect the molecular mechanisms driving the transition from benign adipose tissue expansion to pathological dysfunction, with adipocyte death representing a critical tipping point in this process. This narrative review synthesizes evidence from peer-reviewed literature concerning the emerging role of ferroptosis in adipose tissue dysfunction, examining the core molecular machinery of iron-dependent lipid peroxidation, the GPX4-glutathione defense axis, and the Nrf2-Keap1 cytoprotective pathway within the specific context of obese adipose tissue biology. The analysis reveals that the obese adipose microenvironment, characterized by pathological iron accumulation, enrichment of peroxidation-prone polyunsaturated fatty acid-containing phospholipids, and a chronically besieged antioxidant defense network, creates conditions uniquely favorable to ferroptotic execution. Furthermore, available evidence suggests that signals released from ferroptotic adipocytes are likely to promote macrophage polarization toward a pro-inflammatory phenotype, establishing a self-amplifying pathogenic loop that propagates local and systemic metabolic dysregulation. The review identifies multiple plant-derived nutraceuticals, including curcumin, resveratrol, quercetin, bergamot polyphenolic fraction, sulforaphane, oleuropein, and astaxanthin, as promising multi-targeted modulators capable of intercepting the ferroptotic cascade at the levels of iron catalysis, lipid radical propagation, and Nrf2-dependent antioxidant defense potentiation. These findings position adipocyte ferroptosis as a novel therapeutic target in obesity and support the rationale for mechanism-based nutraceutical interventions aimed at protecting the adipose organ from pathological cell death. Full article

This paper investigates the asymptotic behavior of the solution to a fractional-order Susceptible–Infected–Susceptible (SIS) epidemic model on complete networks. This model couples integer-order and tempered fractional-order derivatives; arises from the generalized continuous-time random walk (CTRW) framework introduced by Angstmann, Henry, and McGann; and is referred to as the Angstmann–Henry–McGann fractional-order SIS model. To handle the difficulties caused by the coupled derivatives in the attractivity analysis, we adopt an approach based on the asymptotic theory of Volterra integro-differential equations with positive-type kernels. By constructing an appropriate Lyapunov functional, we establish the global attractivity of the endemic equilibrium and further discuss its stability. The proposed framework could avoid the complications and difficulties that arise when directly manipulating the differential forms of the models (such as unifying derivatives or extending the state space). Full article

Persistence, coexistence, and boundary transcritical relays are usually studied through model-specific analyses in mathematical epidemiology, ecology, population dynamics, and chemical reaction network theory. Although these fields address closely related questions, they have developed largely independently. This separation is reflected, for example, in the limited mentions of the multi-strain epidemiologic models in ecology’s chemostats and gradostats literature, despite the fact that these are revealed to be very similar once the concept of siphons from chemical reaction network theory is integrated. Conversely, the next-generation matrices and invasion graphs from eco-epidemiology are not mentioned in chemical reaction network theory. Our contribution is firstly conceptual, terminological and definitional: we propose a common framework for the study of boundary phenomena in all positive ODE subfields. We introduce and formalize notions like reproduction and invasion functions attached to siphon faces, relay graphs, relay tables, and boundary transcritical relays. Some of these concepts are known in one of the above fields but largely absent from the others, while others appear to be new; taken together, they suggest a common language for the analysis of boundary phenomena in positive dynamical systems. The usefulness of the framework is illustrated on multi-strain epidemic models like the Feng–Gavish model, for which we derive explicit, testable conditions. For example, invasion of the less fit strain into the fitter strain’s equilibrium is sufficient for coexistence—unconditionally under permanent immunity and together with an explicit feasibility condition on a reduced coexistence polynomial otherwise (for this model, mutual invasibility also ensures persistence; whether invasion is also necessary for coexistence, and explicit further assumptions under which one or the other criterion works for a larger class of models, are still open). Our approach rests on four pillars: (i) Siphon (a CRN concept) geometry, namely, the fact that forward-invariant coordinate faces correspond to siphons, with the disease-free face being the intersection of minimal siphons. (ii) The recently established fact that a transversal Jacobian block on a siphon face is Metzler, which puts under spotlight the roles of its Perron eigenvectors. (iii) A bifurcation theorem linking eigenvalue crossing at a boundary transcritical invasion relay to the emergence of a positive branch on an adjacent face. (iv) Next-generation matrices (NGMs), an ME concept: on siphon faces, NGMs may be defined via regular splittings, and invasibility may be determined by comparing their spectral radii to >1. Full article

Autophagy is a highly conserved degradation and recycling process in eukaryotic cells that plays a critical role in maintaining cellular homeostasis and responding to external stress. During viral infection, autophagy exhibits a classic “double-edged sword” effect—it can act as a host defense mechanism by directly degrading viral components, but it can also be hijacked by viruses to promote their own replication. Porcine epidemic diarrhea virus (PEDV), an important enteric coronavirus that severely affects the global swine industry, engages in a complex and sophisticated interplay with the host autophagy system. This review systematically dissects the dual regulatory mechanisms of autophagy during PEDV infection and reveals two intertwined functional axes. On one hand, PEDV utilizes multiple viral proteins to cooperatively manipulate the autophagic pathway—inducing mitophagy to suppress innate immune responses, utilizing autophagic membranes to construct replication platforms, and blocking autophagic flux to evade degradation—thereby establishing a multi-level pro-viral network. On the other hand, host cells deploy a unified molecular axis of “ubiquitination–autophagy receptor–lysosome” by mobilizing a broad array of restriction factors to target and degrade viral proteins, forming a coordinated defense system. These two axes converge at the oxidative stress–endoplasmic reticulum stress–autophagy hub, where PEDV NSP1 and NSP2 synergistically inhibit the NRF2 antioxidant system to trigger this cascade, while host factors such as DDX6 and ACE2 finely regulate the process. Based on this mechanistic framework, we discuss the therapeutic implications of targeting autophagy for PEDV intervention, with particular emphasis on the development of selective autophagy modulators as potential antiviral agents. We also identify key knowledge gaps and propose future research directions to translate these mechanistic insights into clinical or field applications. This review synthesizes the peer-reviewed literature published between 2013 and 2026, identified through systematic searches of PubMed, Web of Science, and Scopus databases. Notably, the majority of mechanistic findings discussed are derived from in vitro cell culture models, and their translation to in vivo settings remains a significant challenge. Bridging this gap will require validation in physiologically relevant models, such as porcine intestinal organoids and controlled piglet challenge studies, to assess the efficacy and safety of autophagy-targeting interventions in the context of intestinal homeostasis and mucosal immunity. Full article

Persistence, coexistence, competitive exclusion, and global asymptotic stability (GAS) are closely related problems in mathematical epidemiology that are often treated by model-specific arguments. We develop a unified approach to GAS based on Perron–Volterra Lyapunov functions $L_p$, for multi-strain epidemic reaction networks. For bilinear m-strain models with irreducible rank-one infection blocks and block-diagonal next-generation structure, these functions yield a generic competitive-exclusion partition of parameter space into at most $m+1$ regions: either the disease free equilibrium is GAS, or exactly one dominant strain persists and its boundary endemic equilibrium is GAS; see non-generic tie surfaces on which the corresponding reproduction numbers coincide. We also prove a second complete GAS partition, for two-strain models with increasing concave incidence and scalar, non-interacting strain blocks, extending the Rahman–Zou result beyond rational saturating incidence. In this class, the disease-free, single-strain, and coexistence equilibria may all occur, and explicit Lyapunov functions provide the full exclusion/coexistence partition among the four possible equilibrium supports. The construction combines five ingredients: siphons, which determine forward-invariant boundary faces; triangular Jacobian structure on siphon faces; the Metzler property of transversal Jacobians and their Perron eigenvectors; regular next-generation splittings, whose spectral radii determine invasibility; and boundary transcritical invasion relays linking eigenvalue crossings to the emergence of equilibria on adjacent faces. The resulting Perron–Volterra functions combine Volterra entropy terms for resident variables with Perron-weighted linear functionals for absent strain blocks. These constructions are implemented in the Mathematica package EpidCRN, which computes siphons, transversal blocks, invasion data, Perron weights, and candidate Lyapunov functions. For the two model classes considered here, these candidates are proved to be genuine Lyapunov functions and yield complete generic GAS partitions. Full article

Spatio-temporal epidemic forecasting aims to predict future outbreak trajectories across interconnected regions from historical epidemiological observations and meteorological covariates. However, existing approaches often fail to preserve historically salient epidemic states or to fully exploit delayed and region-varying meteorological associations, leading to unstable temporal representations and insufficient meteorological-context-aware spatio-temporal context for prediction at later forecast horizons. In this paper, we propose CASRL, a Climate-Aware Self-Retrospective Representation Learning network for stable and meteorological-context-aware spatio-temporal epidemic forecasting. CASRL first employs a Self-Retrospective Epidemic Encoder (SREE) to retrospectively aggregate historically salient epidemic states through query-guided weighting and adaptive gating, thereby preserving informative historical epidemic states within the look-back window. It then introduces a Climate-Adaptive Graph Message Passing (CAGMP) module that breaks away from traditional passive feature concatenation. Instead, it constructs a separate meteorological-view predictive graph conditioned on the static spatial prior and adaptively fuses it with the incidence-associated topology to model complex cross-regional predictive associations. By integrating self-retrospective epidemic representations with meteorological-view spatio-temporal interactions, CASRL produces forecasts with improved predictive stability at later forecast horizons. Extensive experiments on two public influenza benchmarks show that CASRL is competitive at shorter forecast horizons and provides clearer advantages at later forecast horizons, particularly in phase-alignment-related evaluation and 15-week-ahead forecasting. 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

Flying Ad Hoc Networks let unmanned aerial vehicles communicate directly, without relying on fixed ground infrastructure, in time-critical settings such as disaster response, search and rescue, border surveillance, precision agriculture, and military reconnaissance. UAV mobility, however, causes frequent topology changes and intermittent connectivity, so nodes typically store data locally and replicate it across the network to keep it available. The resulting challenge is consistency: independently evolving copies must be reconciled without a central coordinator, and strong consistency is not realistic in a network this prone to partitioning. We address this with the Decentralized Mobile Reconciliation Protocol (DMRP), which provides eventual consistency among UAV nodes with no external coordination, with convergence formally guaranteed whenever the swarm’s synchronisation graph is eventually connected. DMRP combines immediate local validation and convergence guarantees grounded in conflict-free replicated data type properties; hysteresis-based memory management with dual thresholds to cap journal storage overhead; adaptive delta or full-state synchronisation based on receiver lag; and epidemic propagation for transitive update dissemination. Energy efficiency guided the design throughout, through wireless broadcast and the avoidance of redundant transmissions. DMRP was implemented and evaluated through extensive OMNeT++/INET simulations of three-dimensional FANET scenarios. Results demonstrate that the protocol maintains a strictly bounded reconciliation journal, whereas the reference $\delta$-CRDT log grows without bound, reducing reconciliation-journal storage by up to 75% at the largest workload evaluated, while achieving near-complete consistency after node isolation and network partitioning. Full article

The molecular epidemiology and antiretroviral (ARV) drug resistance of human immunodeficiency virus type 1 (HIV-1) remain incompletely outlined in the Middle East and North Africa (MENA). The aim of this retrospective molecular epidemiology study was to analyze MENA HIV-1 sequences for phylogenetic clustering and to delineate surveillance drug-resistance mutations (SDRMs) for nucleoside reverse-transcriptase inhibitors (NRTIs), non-nucleoside reverse-transcriptase inhibitors (NNRTIs), and protease inhibitors (PIs) across various periods, locations, and subtypes/circulating recombinant forms (CRFs). Viral sequences were retrieved from the Los Alamos HIV Sequence Database as of 15 April 2026. Analyses were done using multiple sub-gene regions (two env regions (n = 224 and n = 60) and PR (n = 2413) and RT (n = 2103) of the pol gene). Phylogeny construction was conducted using maximum-likelihood estimation, while ARV drug resistance analysis was conducted using the Stanford HIVdb algorithm. The HIV-1 MENA sequences showed a remarkable genetic diversity, with co-circulation of multiple subtypes/CRFs, including subtype B in the Maghreb, Levant, and Egypt sub-regions, subtypes A1, G, CRF01_AE, and CRF02_AG in the Gulf Cooperation Council (GCC) and Yemen sub-region, and subtypes C and D in the Horn of Africa and Sudan sub-region. The percentage of MENA HIV-1 sequences in clusters was 10.3% for env1, 8.3% for env2, 22.0% for PR and 37.2% for RT. Phylogenetic reconstruction hinted at a structured epidemic dominated by small transmission units, with most clusters comprising dyads (n = 260) or networks (n = 142) and a limited number of large clusters (n = 8) that were largely confined within national boundaries, with only occasional cross-border linkages (n = 8). Overall SDRM prevalence was 3.2% in the PR region and 14.9% in the RT region, with a higher percentage of NNRTI-associated mutations (10.0%) than NRTI-associated mutations (9.1%) and dual-class resistance observed in 4.1% of sequences. Phylogenetic clustering was not associated with the probability of harboring SDRMs; however, negative binomial models showed that non-clustered sequences had a greater burden of NRTI-associated mutations, whereas no such association was observed for NNRTI- or PI-associated mutations. The findings showed predominantly localized and fragmented MENA HIV-1 transmission dynamics. Heterogeneous ARV drug resistance dynamics indicated that resistance emergence might be shaped by broader epidemiologic and treatment-related factors rather than ongoing clustered transmission. There is a need for coordinated molecular surveillance and optimized ART strategies across the MENA countries. 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

Background/Objectives: The epidemiology of carbapenem-resistant Klebsiella pneumoniae (CR-Kp) in Europe is evolving towards an increasing contribution of metallo-β-lactamases (MBLs). In particular, co-production of New Delhi metallo-β-lactamase (NDM) and OXA-48-like carbapenemases represents a major concern due to limited therapeutic options and epidemic potential. We aimed to describe temporal trends and genomic characteristics of NDM and OXA-48-like co-producing K. pneumoniae within a regional surveillance programme targeting ceftazidime-avibactam (CZA)-resistant carbapenem-resistant Enterobacterales (CRE) in the Latium Region, Italy. Methods: Between January 2019 and December 2025, CZA-resistant CRE isolates were collected through a regional surveillance network. Antimicrobial susceptibility testing and carbapenemase detection were performed, and NDM-producing K. pneumoniae (NDM-Kpn) was analysed by whole-genome sequencing (WGS). Genomic analyses included multi-locus sequence typing, assessment of clonal relatedness, and resistome/virulome profiling. Results: A total of 2752 non-repetitive CZA-resistant CRE were collected. The analysis of CZA-resistant K. pneumoniae isolates submitted to the regional surveillance network showed that the proportion of NDM producers increased markedly from 2023 onwards. In particular, NDM in association with OXA-48-like reached 26.0% in 2024 and 43.6% in 2025, becoming the predominant carbapenemase profile within this selected surveillance population. WGS of 437 NDM-Kpn revealed a structured population dominated by Sequence Type (ST)147 (63.2%), widely disseminated across 24 hospitals and characterised by a predominant NDM-1 variant and OXA-48-like co-producing profile associated with KL10/wzi420 capsular type. A subset of isolates, mainly within the ST147-KL64 subgroup, showed higher virulence scores, indicating a possible convergence of resistance and virulence. Conclusions: Our findings indicate a rapid shift towards NDM-mediated resistance among CZA-resistant K. pneumoniae submitted to the regional surveillance network, with the emergence of NDM and OXA-48-like co-producing isolates associated with a dominant ST147 clone detected across multiple hospitals. These results highlight the urgent need for coordinated genomic surveillance and infection prevention strategies. Full article

Civilian communication systems often fail during armed conflicts, political unrest, and large-scale Internet disruptions—precisely when reliable communication is most needed. This paper presents HERMES, a resilient hybrid communication architecture that integrates HTTP/IP networking, Bluetooth Low Energy (BLE) mesh communication, and Delay-Tolerant Networking (DTN) within a unified adaptive routing framework. Unlike conventional approaches that treat alternative transports as backup solutions, HERMES dynamically selects the most efficient transport path based on current network conditions using a transport-aware forwarding policy whose cost function combines round-trip time, transport preference, and observed link risk. The architecture is built on distributed microservices that support topology discovery, shortest-path routing, and fault-tolerant message delivery. Reliability is enhanced through acknowledgments, bounded retransmissions, duplicate suppression, and graceful degradation mechanisms, while end-to-end authenticated encryption (Noise XX with a Double Ratchet) ensures secure communication across transport changes. A prototype implementation developed in C# on .NET 9 was evaluated on a five-node testbed, and a custom Network Simulator 3 (NS-3) module was used to extend the evaluation to networks of up to 500 nodes, under multiple failure scenarios, including node crashes, network partitioning, and complete Internet outages. Experimental results show that HERMES maintains perfect or near-perfect delivery in static topologies, including during a complete Internet blackout that disables IP-only messaging. Compared with the published Delay-Tolerant Networking protocols Epidemic and PRoPHET at one hundred nodes, HERMES exceeds their delivery ratio in static and failure scenarios and remains within 0.06 of them under pedestrian mobility during blackout, while transmitting roughly 35× fewer bytes– and about 21× fewer even relative to the more bandwidth-efficient MaxProp baseline. Under coordinated drop attacks by adversarial relays, HERMES degrades gracefully where flooding-based baselines collapse. This approach demonstrates that resilient civilian communication can be effectively achieved through metric-driven adaptive multi-transport routing, making it suitable for disaster recovery, contested environments, and connectivity-limited regions. Full article

This paper develops a spectral framework for analyzing epidemic dynamics on weighted networks through the Kirchhoff index and the Laplacian spectrum. Starting from a nonlinear network-based SIS model, we investigate the disease-free and endemic equilibria and establish their local stability conditions in terms of the spectral radius of the adjacency matrix. We then introduce a spectral criterion based on the Kirchhoff index, deriving bounds that connect the total effective resistance of the network with the algebraic connectivity and the characteristic relaxation time. A dimensionless parameter combining epidemic transmission and network topology is proposed, leading to a critical Kirchhoff threshold that separates highly resilient networks from weakly connected and more sensitive structures. These results are summarized in the Kirchhoff Stability Principle, which provides a unified relationship between the Kirchhoff index, algebraic connectivity, relaxation time, and dynamical robustness. Numerical illustrations on several canonical graph topologies, including complete, star, cycle, and path graphs, validate the theoretical findings and demonstrate that networks with smaller Kirchhoff indices exhibit faster convergence and stronger resilience against perturbations. The proposed framework offers a simple spectral approach for understanding the interplay between graph topology and epidemic dynamics and can be extended to more general epidemic and network models. Full article