arXiv subjects

Fabio Sanchez

Publications and source records attributed to Fabio Sanchez.

At least 19 recordsLinked to original sources

arXiv2026

Network amplification of dengue declines as endemicity rises: climate-adjusted directional spread across Costa Rican cantons, 1993-2012

\textbf{Background:} In Costa Rica, dengue is reported and controlled at the canton level, and outbreaks in one canton are often followed by outbreaks in others. Climate models describe where conditions favor transmission but not how dengue moves \emph{between} places, the directional, between-place spread that shapes where an outbreak travels next. \noindent \textbf{Methods:} From weekly case counts for all 81 cantons (1993--2012; \num{246524} cases) we reconstructed a canton-to-canton spread map using the roughly three-week dengue generation interval, removed the shared seasonal and climatic signal so that only direction-specific spread remained, and summarized it by the receiving and source cantons, an amplification factor, and a directionality index, tracked over five-year windows. \noindent \textbf{Results:} Climate-adjusted spread is strongly directional and concentrates in the lowland Caribbean and Pacific cantons (Lim\'on, Matina, Gu\'acimo, Garabito, Orotina). A local outbreak is amplified about three- to fourfold across the network even though overall transmission is not growing. This amplification was greatest during the emergence phase of the 1990s and declined markedly as annual reported cases increased, while the \emph{direction} of spread remained fixed; the decline persists after controlling for the broadening of surveillance coverage. \noindent \textbf{Conclusions:} Routine surveillance alone can map which cantons tend to experience dengue and the pathways through which it appears to spread, providing a potential input for prioritizing surveillance and vector control, particularly when a serotype or the disease itself is newly establishing. As a historical description of average behavior over multi-year windows, it is a planning input whose prospective value remains to be tested.

q-bio.PE↗

arXiv2026

What $R_0$ Deletes: Eigenvectors, Non-Normality, and the Social Content of the Basic Reproduction Number

The basic reproduction number is the spectral radius of a matrix, $R_0=\rho(K)$. Taking that definition literally, we ask what $K\mapsto\rho(K)$ discards. A matrix carries three kinds of information: its dominant eigenvalue, its dominant eigenvectors, and its departure from normality. $R_0$ keeps only the first; the other two are where the epidemic's social structure lives. The right eigenvector is the burden distribution, the left the source distribution; they coincide when the system is normal and diverge under heterogeneity. Across the $177$ national contact matrices of Prem et al., the operator is \emph{never} normal, and once age-specific susceptibility is included, its source and burden eigenvectors are misaligned by a median of $26^{\circ}$, exceeding $40^{\circ}$ in some countries: the groups that drive transmission are systematically not those that bear it. We prove that under reciprocal contact this misalignment obeys a Kantorovich bound set by the susceptibility contrast $q_{\max}/q_{\min}$ alone, and zero when susceptibility is uniform, with the excess in real, non-reciprocal matrices contributed by contact asymmetry. Transient amplification, by contrast, stays small, so the operative social content is the misalignment, not transient blow-up. The omission also has teeth: because minimizing $R_0$ protects those who \emph{spread} infection, while minimizing deaths protects those who \emph{die} from it, the two target different age groups; the former sometimes raises average infection fatality even as it lowers the scalar. When contact is strongly structured and susceptibility is heterogeneous, we suggest reporting $R_0$ along with its eigenvectors rather than reporting it alone.

math.DS↗

arXiv2026

When Self-Protection Backfires: Adaptive Contact Behavior Expands the Endemic Basin in an Addiction Model with Nonlinear Relapse

We extend the Susceptible--Addicted--Reformed (SAR) model of \cite{sanchez2023}, which exhibits a forward--backward bifurcation driven by nonlinear relapse, by embedding an epi-economic behavioral layer in the spirit of \cite{fenichel2011}. At-risk individuals choose contact levels by solving a finite-horizon dynamic program that balances the utility of social activity against the expected cost of addiction. We prove that the basic reproduction number $ R_0 $ and the local stability of the addiction-free equilibrium remain unchanged by the behavioral layer. However, the endemic structure is fundamentally altered: the behavioral response collapses exactly to a scalar mixing factor $ M $, and the bifurcation curve factorizes as $ R_0(a) = R_{\rm cl}(a)/M(a) $. This yields an exact comparison principle: the saddle-node fold shifts to lower $ R_0 $ (enlarging the endemic basin) if and only if $ M \ge 1 $ along the branch. For rational self-protective behavior under conditional proportional mixing, we prove $ M \ge 1 $, so the basin enlarges; the opposite holds under frequency-dependent mixing. Numerical continuation shows that, at baseline parameters, the fold moves left by $ \Delta R_0 \approx -0.035 $ and the critical initial addiction level drops by 2--6 percentage points. Gillespie simulations confirm that the enlarged basin increases the stochastic probability of addiction establishment by up to threefold near threshold. This counterintuitive result that rational self-protection can make addiction easier to establish has direct implications for prevention policy.

math.DS↗

arXiv2025

Localized risk perception triggers early behavioral adaptations in epidemics on networks

The contact structure of the population shapes the progression of epidemics. Nonetheless, the joint evolution of individual behavioral adaptations and disease dynamics on networks remains poorly understood. We use a behavioral-epidemiological model to study the joint evolution of human behavior and epidemic dynamics on networks. Our results reveal how the adaptation of local social structures, influenced by risk-benefit trade-offs, affects the dynamics of epidemics. We allow the epidemic and population-level behavior dynamics to emerge from the heterogeneous behavioral responses of individuals. Our framework assumes that individuals adjust their contact structure by temporarily dropping or maintaining connections based on perceived benefits and risks. Our results show that behavioral responses induced by localized risk perceptions lead to premature population-level responses relative to epidemic dynamics. Specifically, individual efforts peak at the epidemic maximum, while population-level efforts remain modest. We explore the robustness and extensions incorporating heterogeneous subpopulations.

physics.soc-ph↗

arXiv2025

Modeling Bulimia Nervosa in the Digital Age: The Role of Social Media

Globalization has fundamentally reshaped societal dynamics, influencing how individuals interact and perceive themselves and others. One significant consequence is the evolving landscape of eating disorders such as bulimia nervosa (BN), which are increasingly driven not just by internal psychological factors but by broader sociocultural and digital contexts. While mathematical modeling has provided valuable insights, traditional frameworks often fall short in capturing the nuanced roles of social contagion, digital media, and adaptive behavior. This review synthesizes two decades of quantitative modeling efforts, including compartmental, stochastic, and delay-based approaches. We spotlight foundational work that conceptualizes BN as a socially transmissible condition and identify critical gaps, especially regarding the intensifying impact of social media. Drawing on behavioral epidemiology and the adaptive behavior framework by Fenichel et al., we advocate for a new generation of models that incorporate feedback mechanisms, content-driven influence functions, and dynamic network effects. This work outlines a roadmap for developing more realistic, data-informed models that can guide effective public health interventions in the digital era.

cs.SI↗

arXiv2025

A Dynamical Systems Analysis of Trap Music Exposure and School Dropout Among Costa Rican Adolescents

In recent years, a surge in the popularity of trap music among adolescents has prompted concerns about its potential influence on youth behavior and educational outcomes. In this study, we develop a novel compartmental model using a system of differential equations to explore the relationship between exposure to trap music and school dropout rates among Costa Rican adolescents aged 13 to 17. The model divides the population into distinct compartments representing susceptible individuals, casual listeners, active participants, those exhibiting risk-associated behaviors, and ultimately, school dropouts. Key parameters, including transmission via peer influence, progression rates between exposure stages, and recovery dynamics, capture the complex interplay between cultural diffusion and behavioral change. Analytical investigation of the basic reproductive number, $R_0$, and both trap-free and endemic equilibrium states provide insight into the conditions under which the influence of trap music proliferates. Numerical simulations, implemented in MATLAB, further illustrate how parameter variations, especially the potential for recovery, affect the system's dynamics. Our results suggest that although exposure to trap music is widespread, the progression to adverse behavioral outcomes leading to school dropout is highly sensitive to intervention strategies, offering valuable implications for educational policy and targeted preventive measures.

physics.soc-ph↗

arXiv2025

The nexus between disease surveillance, adaptive human behavior and epidemic containment

Epidemics exhibit interconnected processes that operate at multiple time and organizational scales, a hallmark of complex adaptive systems. Modern epidemiological modeling frameworks incorporate feedback between individual-level behavioral choices and centralized interventions. Nonetheless, the realistic operational course for disease detection, planning, and response is often overlooked. Disease detection is a dynamic challenge, shaped by the interplay between surveillance efforts and transmission characteristics. It serves as a tipping point that triggers emergency declarations, information dissemination, adaptive behavioral responses, and the deployment of public health interventions. Evaluating the impact of disease surveillance systems as triggers for adaptive behavior and public health interventions is key to designing effective control policies. We examine the multiple behavioral and epidemiological dynamics generated by the feedback between disease surveillance and the intertwined dynamics of information and disease propagation. Specifically, we study the intertwined dynamics between: $(i)$ disease surveillance triggering health emergency declarations, $(ii)$ risk information dissemination producing decentralized behavioral responses, and $(iii)$ centralized interventions. Our results show that robust surveillance systems that quickly detect a disease outbreak can trigger an early response from the population, leading to large epidemic sizes. The key result is that the response scenarios that minimize the final epidemic size are determined by the trade-off between the risk information dissemination and disease transmission, with the triggering effect of surveillance mediating this trade-off. Finally, our results confirm that behavioral adaptation can create a hysteresis-like effect on the final epidemic size.

math.DS↗

arXiv2024

Interplay between Foraging Choices and Population Growth Dynamics

In this study, we couple a population dynamics model with a model for optimal foraging to study the interdependence between individual-level cost-benefits and population-scale dynamics. Specifically, we study the logistic growth model, which provides insights into population dynamics under resource limitations. Unlike exponential growth, the logistic model incorporates the concept of carrying capacity, thus offering a more realistic depiction of biological populations as they near environmental limits. We aim to study the impact of individual-level incentives driving behavioral responses in a dynamic environment. Specifically, explore the coupled dynamics between population density and individuals' foraging times. Our results yield insights into the effects of population size on individuals' optimal foraging efforts, which impacts the population's size.

q-bio.PE↗

arXiv2024

Stochastic two-patch epidemic model with nonlinear recidivism

We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random transmission, recovery, and inter-patch movement fluctuations. We showcase the interplay between local dynamics and migration effects on disease persistence using Monte Carlo simulations and three stochastic approximations-discrete-time Markov chain (DTMC), Poisson, and stochastic differential equations (SDE). Our analysis shows that stochastic effects can cause extinction events and oscillations near critical thresholds like the basic reproduction number, R0, phenomena absent in deterministic models. Numerical simulations highlight source-sink dynamics, where one patch is a persistent infection source while the other experiences intermittent outbreaks.

q-bio.PE↗

arXiv2024

Source-sink dynamics in a two-patch SI epidemic model with life stages and no recovery from infection

This study presents a comprehensive analysis of a two-patch, two-life stage SI model without recovery from infection, focusing on the dynamics of disease spread and host population viability in natural populations. The model, inspired by real-world ecological crises like the decline of amphibian populations due to chytridiomycosis and sea star populations due to Sea Star Wasting Disease, aims to understand the conditions under which a sink host population can present ecological rescue from a healthier, source population. Mathematical and numerical analyses reveal the critical roles of the basic reproductive numbers of the source and sink populations, the maturation rate, and the dispersal rate of juveniles in determining population outcomes. The study identifies conditions for disease-free, endemic, and extinction equilibria in sink populations, emphasizing the potential for ecological and evolutionary mechanisms to facilitate coexistence or recovery. These findings provide insights into managing natural populations affected by disease, with implications for conservation strategies, such as the importance of maintaining reproductively viable refuge populations and considering the effects of dispersal and maturation rates on population recovery. The research underscores the complexity of host-pathogen dynamics in spatially structured environments and highlights the need for multi-faceted approaches to biodiversity conservation in the face of emerging diseases.

q-bio.PE↗

arXiv2023

A nonlinear relapse model with disaggregated contact rates: analysis of a forward-backward bifurcation

We developed a nonlinear differential equation model to explore the dynamics of relapse phenomena. Our incidence rate function is formulated, taking inspiration from recent adaptive algorithms. It incorporates contact behavior for individuals in each health class. We use constant contact rates at each health status for our analytical results and prove conditions for different forward-backward bifurcation scenarios. The relationship between the different contact rates influences these conditions. Numerical examples show the sensitivity of the model toward initial conditions. In particular, we highlight the effect of temporarily recovered individuals and infected initial conditions.

math.DS↗

arXiv2023

Bayesian spatio-temporal model with INLA for dengue fever risk prediction in Costa Rica

Due to the rapid geographic spread of the Aedes mosquito and the increase in dengue incidence, dengue fever has been an increasing concern for public health authorities in tropical and subtropical countries worldwide. Significant challenges such as climate change, the burden on health systems, and the rise of insecticide resistance highlight the need to introduce new and cost-effective tools for developing public health interventions. Various and locally adapted statistical methods for developing climate-based early warning systems have increasingly been an area of interest and research worldwide. Costa Rica, a country with micro-climates and endemic circulation of the dengue virus (DENV) since 1993, provides ideal conditions for developing projection models with the potential to help guide public health efforts and interventions to control and monitor future dengue outbreaks.

stat.AP↗

arXiv2023

Common patterns between dengue cases, climate, and local environmental variables in Costa Rica: A Wavelet Approach

Throughout history, prevention and control of dengue transmission have challenged public health authorities worldwide. In the last decades, the interaction of multiple factors, such as environmental and climate variability, has influenced increments in incidence and geographical spread of the virus. In Costa Rica, a country characterized by multiple microclimates separated by short distances, dengue has been endemic since its introduction in 1993. Understanding the role of climatic and environmental factors in the seasonal and inter-annual variability of disease spread is essential to develop effective surveillance and control efforts. In this study, we conducted a wavelet time series analysis of weekly climate, local environmental variables, and dengue cases (2001-2019) from 32 cantons in Costa Rica to identify significant periods (e.g., annual, biannual) in which climate and environmental variables co-varied with dengue cases. Wavelet coherence analysis was used to characterize seasonality, multi-year outbreaks, and relative delays between the time series. Results show that dengue outbreaks occurring every 3 years in cantons located in the country's Central, North, and South Pacific regions were highly coherent with the Oceanic Niño 3.4 and the Tropical North Caribbean Index (TNA). Dengue cases were in phase with El Niño 3.4 and TNA, with El Niño 3.4 ahead of dengue cases by roughly nine months and TNA ahead by less than three months. Annual dengue outbreaks were coherent with local environmental variables (NDWI, EVI, Evapotranspiration, and Precipitation) in most cantons except those located in the Central, South Pacific, and South Caribbean regions of the country. The local environmental variables were in phase with dengue cases and were ahead by around three months.

q-bio.PE↗

arXiv2022

A mathematical model with nonlinear relapse: conditions for a forward-backward bifurcation

We constructed a Susceptible-Addicted-Reformed model and explored the dynamics of nonlinear relapse in the Reformed population. The transition from susceptible considered {\it at-risk} is modeled using a strictly decreasing general function, mimicking an influential factor that reduces the flow into the addicted class. The {\it basic reproductive number} is computed. Furthermore, $R_0$ determines the local asymptotically stability of the addicted-free equilibrium. Conditions for a forward-backward bifurcation were established using $R_0$ and other threshold quantities. A stochastic version of the model is presented, and some numerical examples are shown. Results showed that the influence of the temporarily reformed individuals is highly sensitive to the initial addicted population.

math.DS↗

arXiv2022

A multilayer network model of Covid-19: implications in public health policy in Costa Rica

Successful partnerships between researchers, experts and public health authorities has been critical to navigate the challenges of the Covid-19 pandemic worldwide. In Costa Rica, we constructed a multilayer network model that incorporates a diverse contact structure for each individual (node). The different layers which constitute the individual's contact structure include: family, friends, and sporadic interactions. Different scenarios were constructed to forecast and have a better understanding of the possible routes of the pandemic in the country, given the information that was available at the time and the different measures implemented by the health authorities of the country. Strong collaboration within our diverse team allowed using the model to tailor advice on contingency measures to health authorities. The model helped develop informed strategies to prepare the public health system in Costa Rica. The development, evolution and applications of a multilayer network model of Covid-19 in the adoption of sanitary measures in Costa Rica has been an example of the potential of such partnerships.

physics.soc-ph↗

arXiv2022

Assessing dengue fever risk in Costa Rica by using climate variables and machine learning techniques

Dengue fever is a vector-borne disease mostly endemic to tropical and subtropical countries that affect millions every year and is considered a significant burden for public health. Its geographic distribution makes it highly sensitive to climate conditions. Here, we explore the effect of climate variables using the Generalized Additive Model for location, scale, and shape (GAMLSS) and Random Forest (RF) machine learning algorithms. Using the reported number of dengue cases, we obtained reliable predictions. The uncertainty of the predictions was also measured. These predictions will serve as input to health officials to further improve and optimize the allocation of resources prior to dengue outbreaks.

cs.CY↗

arXiv2021

The Role of SARS-CoV-2 Testing on Hospitalizations in California

The rapid spread of the new SARS-CoV-2 virus triggered a global health crisis disproportionately impacting people with pre-existing health conditions and particular demographic and socioeconomic characteristics. One of the main concerns of governments has been to avoid the overwhelm of health systems. For this reason, they have implemented a series of non-pharmaceutical measures to control the spread of the virus, with mass tests being one of the most effective control. To date, public health officials continue to promote some of these measures, mainly due to delays in mass vaccination and the emergence of new virus strains. In this study, we studied the association between COVID-19 positivity rate and hospitalization rates at the county level in California using a mixed linear model. The analysis was performed in the three waves of confirmed COVID-19 cases registered in the state to September 2021. Our findings suggest that test positivity rate is consistently associated with hospitalization rates at the county level for all waves of study. Demographic factors that seem to be related with higher hospitalization rates changed over time, as the profile of the pandemic impacted different fractions of the population in counties across California.

stat.AP↗

arXiv2021

Projecting the Impact of Covid-19 Variants and Vaccination Strategies in Disease Transmission using a Multilayer Network Model in Costa Rica

For countries starting to receive steady supplies of vaccines against SARS-CoV-2, the course of Covid-19 for the following months will be determined by the emergence of new variants and successful roll-out of vaccination campaigns. To anticipate this scenario, we used a multilayer network model developed to forecast the transmission dynamics of Covid-19 in Costa Rica, and to estimate the impact of the introduction of the Delta variant in the country, under two plausible vaccination scenarios, one sustaining Costa Rica's July 2021 vaccination pace of 30,000 doses per day and with high acceptance from the population and another with declining vaccination pace to 13,000 doses per day and with lower acceptance. Results suggest that the introduction and gradual dominance of the Delta variant would increase Covid-19 hospitalizations and ICU admissions between $35\%$ and $33.25\%$, from August 2021 to December 2021, depending on vaccine administration and acceptance. In the presence of the Delta variant, new Covid-19 hospitalizations and ICU admission would experience an average increase of $24.26\%$ and $27.19\%$ respectively in the same period if the vaccination pace drops. Our results can help decision-makers better prepare for the COVID-19 pandemic in the months to come.

q-bio.PE↗