arXiv subjects

Enrique C. Gabrick

Publications and source records attributed to Enrique C. Gabrick.

16 recordsLinked to original sources

arXiv2026

Non-Markovian Light-Matter Dynamics in the Time Fractional Jaynes-Cummings Model with Modulated Coupling

We investigate the fractional time description of a generalized quantum light-matter system modeled by a time-dependent Jaynes-Cummings (JC) interaction, with different coupling types: constant, linear, exponential, and sinusoidal. Two formulations of the time fractional Schrödinger equation (TFSE) are examined, with a focus on their impact on population inversion and entanglement. Our findings highlight that the introduction of fractional order introduces memory effects, associated with damped oscillations and asymptotic decay. Furthermore, we find that the time-dependent couplings, combined with distinct fractional formulations, influence how these effects occur, ultimately resulting in high or low entanglement. A key finding of our work is that, under sinusoidal coupling, non-periodic dynamics is preserved for both formulations of the TFSE; however, within a certain range, the fractional order can act as a control mechanism for the non-periodic evolution.

physics.gen-ph↗

arXiv2026

Climate and dengue synchronization in southern Brazil: a municipal analysis with cross-state validation

Dengue transmission is rapidly expanding beyond its historical tropical range, raising concerns about how climate change may alter the collective dynamics of epidemics. While most studies focus on transmission risk, much less is known about how climate affects the synchronization of outbreaks. In this work, we investigate dengue synchronization using epidemiological and climate data from 74 municipalities in the state of Paraná (southern Brazil) between 2010 and 2024. We quantify outbreak coherence using the Event Synchronization (ES) method. Our results reveal a transition from a low-transmission regime to a high-transmission regime accompanied by a marked increase in synchronization across cities. We also show that climate anomalies increase the number of permissive days for dengue transmission. Our results suggest that such days are significantly associated with outbreak synchronization. We identify a two-stage climate mechanism: conducive climatic conditions first reduce the probability of asynchronous states and coincide with the emergence of synchronized outbreaks, and subsequently sustain higher synchronization levels. Extending the analysis through comparative analyses in Ceará and Minas Gerais, we uncover that climate consistently amplifies synchronization, although its role in the onset of synchronization depends on regional climatic regimes. These findings highlight climate-driven synchronization as an emerging feature shaping dengue dynamics.

physics.soc-ph↗

arXiv2026

Stochastic reversal of deterministic selection in epidemic strain competition

Different strains competing for a common pool of susceptible individuals is a key problem in mathematical epidemiology. To address this problem, we investigate a two-strain model within a Susceptible-Infected-Recovered (SIR) framework. While classical deterministic theory predicts that the basic reproduction number fully determines selection, we show that stochastic effects play a key role in the dynamics. We discover that stochastic fluctuations can reverse the deterministic advantage even far from the quasi-neutral regime. Further, we find that stochasticity drastically reduces fixation times from years, in the deterministic case, to days. The fixation time is non-linearly proportional to the noise intensity and the distance from the quasi-neutral regime, following a universal rule obtained from a scaling law. The nature of the problem and the equations allow us to interpret the competition as a dynamical evolution around an effective potential, with the potential barrier corresponding to the unstable manifold associated with the coexistence. Even in a stable situation of dominance of one strain, the noise can induce crossings through the potential. We find that the reversal can occur even far from the quasi-neutral regime with significant probability.

q-bio.PE↗

arXiv2025

Predicting temperatures in Brazilian states capitals via Machine Learning

Climate change refers to substantial long-term variations in weather patterns. In this work, we employ a Machine Learning (ML) technique, the Random Forest (RF) algorithm, to forecast the monthly average temperature for Brazilian's states capitals (27 cities) and the whole country, from January 1961 until December 2022. To forecast the temperature at $k$-month, we consider as features in RF: $i)$ global emissions of carbon dioxide (CO$_2$), methane (CH$_4$), and nitrous oxide (N$_2$O) at $k$-month; $ii)$ temperatures from the previous three months, i.e., $(k-1)$, $(k-2)$ and $(k-3)$-month; $iii)$ combination of $i$ and $ii$. By investigating breakpoints in the time series, we discover that 24 cities and the gases present breakpoints in the 80's and 90's. After the breakpoints, we find an increase in the temperature and the gas emission. Thereafter, we separate the cities according to their geographical position and employ the RF algorithm to forecast the temperature from 2010-08 until 2022-12. Based on $i$, $ii$, and $iii$, we find that the three inputs result in a very precise forecast, with a normalized root mean squared error (NMRSE) less than 0.083 for the considered cases. From our simulations, the better forecasted region is Northeast through $iii$ (NMRSE = 0.012). Furthermore, we also investigate the forecasting of anomalous temperature data by removing the annual component of each time series. In this case, the best forecasting is obtained with strategy $i$, with the best region being Northeast (NRMSE = 0.090).

physics.ao-ph↗

arXiv2025

Continuous and discrete compartmental models for infectious disease

The study of infectious disease propagation is essential for understanding and controlling epidemics. One of the most useful tools for gaining insights into the spread of infectious diseases is mathematical modelling. In terms of mathematical epidemiology, the main models are based on compartments, such as SI, SIR, and SEIR. These models offer mathematical frameworks for representing the proliferation dynamics of various diseases, for instance flu and smallpox. In this work, we explore these models using two distinct mathematical approaches, Cellular Automata (CA) and ODEs. They are able to reproduce the spread dynamics of diseases with their own individuality. CA models incorporate the local interaction among individuals with discrete time and space, while ODEs provide a continuous and simplified view of a disease propagation in large and homogeneous populations. By comparing these two approaches, we find that the shape of the curves of all models is similar for both representations. Although, the growth rates differ between CA and ODE. One of our results is to show that the CA yields a power-law growth, while the ODE growth rate is well-represented by an exponential function. Furthermore, a substantial contribution of our work is using a hyperbolic tangent to fit the initial growth of infected individuals for all the considered models. Our results display a strong correlation between simulated data and adjusted function. We mainly address this successful result by the fact that the hyperbolic function captures both growing: the power-law (when considered the first terms of infinite sums) and combinations of exponential (when the hyperbolic function is written via exponential). Therefore, our work shows that when modelling a disease the choice of mathematical representation is crucial, in particular to model the onset of an epidemic.

q-bio.PE↗

arXiv2024

Fractional and fractal extensions of epidemiological models

One way to study the spread of disease is through mathematical models. The most successful models compartmentalize the host population according to their infectious stage, e.g., susceptible (S), infected (I), exposed (E), and recovered (R). The composition of these compartments leads to the SI, SIS, SIR, and SEIR models. In this Chapter, we present and compare three formulations of SI, SIS, SIR, and SEIR models in the framework of standard (integer operators), fractional (Caputo sense), and fractal derivatives (Hausdorff sense). As an application of the SI model, we study the evolution of AIDS cases in Bangladesh from 2001 to 2021. For this case, our simulations suggest that fractal formulation describes the data well. For the SIS model, we consider syphilis data from Brazil from 2006 to 2017. In this case, the three frameworks describe the data with good accuracy. We used data from Influenza A to adjust the SIR model in previous approaches and observed that the fractional formulation was better. The last application considers the COVID-19 data from India in the range 2020-04-10 to 2020-12-31 to adjust the parameters of the SEIR model. The standard formulation fits the data better than the other approaches. As a common result, all models exhibit steady solutions in the different formulations. The time to reach a steady solution is correlated to the considered approach. The standard and fractal formulations reach the steady state earlier when compared with the fractional formulation.

q-bio.PE↗

arXiv2024

Control, bi-stability and preference for chaos in time-dependent vaccination campaign

In this work, effects of constant and time-dependent vaccination rates on the Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) seasonal model are studied. Computing the Lyapunov exponent, we show that typical complex structures, such as shrimps, emerge for given combinations of constant vaccination rate and another model parameter. In some specific cases, the constant vaccination does not act as a chaotic suppressor and chaotic bands can exist for high levels of vaccination (e.g., $> 0.95$). Moreover, we obtain linear and non-linear relationships between one control parameter and constant vaccination to establish a disease-free solution. We also verify that the total infected number does not change whether the dynamics is chaotic or periodic. The introduction of a time-dependent vaccine is made by the inclusion of a periodic function with a defined amplitude and frequency. For this case, we investigate the effects of different amplitudes and frequencies on chaotic attractors, yielding low, medium, and high seasonality degrees of contacts. Depending on the parameters of the time-dependent vaccination function, chaotic structures can be controlled and become periodic structures. For a given set of parameters, these structures are accessed mostly via crisis and in some cases via period-doubling. After that, we investigate how the time-dependent vaccine acts in bi-stable dynamics when chaotic and periodic attractors coexist. We identify that this kind of vaccination acts as a control by destroying almost all the periodic basins. We explain this by the fact that chaotic attractors exhibit more desirable characteristics for epidemics than periodic ones in a bi-stable state.

physics.bio-ph↗

arXiv2024

When climate variables improve the dengue forecasting: a machine learning approach

Dengue is a viral vector-borne infectious disease that affects many countries worldwide, infecting around 390 million people per year. The main outbreaks occur in subtropical and tropical countries. We study here the influence of climate on dengue in Natal (2016-2019), Brazil, Iquitos (2001-2012), Peru, and Barranquilla (2011-2016), Colombia. For the analysis and simulations, we apply Machine Learning (ML) techniques, especially the Random Forest (RF) algorithm. In addition, regarding a feature in the ML technique, we analyze three possibilities: only dengue cases (D); climate and dengue cases (CD); humidity and dengue cases (HD). Depending on the city, our results show that the climate data can improve or not the forecast. For instance, for Natal, D induces a better forecast. For Iquitos, it is better to use CD. Nonetheless, for Barranquilla, the forecast is better, when we include cases and humidity data. For Natal, when we use more than 64\% and less than 80\% of the time series for training, we obtain results with correlation coefficients ($r$) among 0.917 and 0.949 and mean absolute errors (MAE) among 57.783 and 71.768 for the D case in forecasting. The optimal range for Iquitos is obtained when 79\% up to 88\% of the time series is considered for training. For this case, the best case is CD, having a minimum $r$ equal to 0.850 and maximum 0.887, while values of MAE oscillate among 2.780 and 4.156. For Barranquilla, the optimal range occurs between 72\% until 82\% of length training. In this case, the better approach is HD, where the measures exhibit a minimum $r$ equal to 0.942 and a maximum 0.953, while the minimum and maximum MAE vary between 6.085 and 6.669. We show that the forecast of dengue cases is a challenging problem and climate variables do not always help. However, when we include the mentioned climate variables, the most important one is humidity.

physics.bio-ph↗

arXiv2024

Spiral wave dynamics in a neuronal network model

Spiral waves are spatial-temporal patterns that can emerge in different systems as heart tissues, chemical oscillators, ecological networks and the brain. These waves have been identified in the neocortex of turtles, rats, and humans, particularly during sleep-like states. Although their functions in cognitive activities remain until now poorly understood, these patterns are related to cortical activity modulation and contribute to cortical processing. In this work, we construct a neuronal network layer based on the spatial distribution of pyramidal neurons. Our main goal is to investigate how local connectivity and coupling strength are associated with the emergence of spiral waves. Therefore, we propose a trustworthy method capable of detecting different wave patterns, based on local and global phase order parameters. As a result, we find that the range of connection radius (R) plays a crucial role in the appearance of spiral waves. For R < 20 μm, only asynchronous activity is observed due to small number of connections. The coupling strength (gsyn ) greatly influences the pattern transitions for higher R, where spikes and bursts firing patterns can be observed in spiral and non-spiral waves. Finally, we show that for some values of R and gsyn bistable states of wave patterns are obtained.

physics.bio-ph↗

arXiv2024

Impact of periodic vaccination in SEIRS seasonal model

We study three different strategies of vaccination in a SEIRS (Susceptible--Exposed--Infected--Recovered--Susceptible) seasonal forced model, which are: ($i$) continuous vaccination; ($ii$) periodic short time localized vaccination and ($iii$) periodic pulsed width campaign. Considering the first strategy, we obtain an expression for the basic reproduction number and infer a minimum vaccination rate necessary to ensure the stability of the disease-free equilibrium (DFE) solution. In the second strategy, the short duration pulses are added to a constant baseline vaccination rate. The pulse is applied according to the seasonal forcing phases. The best outcome is obtained by locating the intensive immunization at inflection of the transmissivity curve. There, a vaccination rate of $44.4\%$ of susceptible individuals is enough to ensure DFE. For the third vaccination proposal, additionally to the amplitude, the pulses have a prolonged time width. We obtain a non-linear relationship between vaccination rates and the duration of the campaign. Our simulations show that the baseline rates, as well as the pulse duration, can substantially improve the vaccination campaign effectiveness. These findings are in agreement with our analytical expression. We show a relationship between the vaccination parameters and the accumulated number of infected individuals, over the years and show the relevance of the immunisation campaign annual reaching for controlling the infection spreading. Regarding the dynamical behaviour of the model, our simulations shows that chaotic and periodic solutions, as well as bi-stable regions, depend on the vaccination parameters range.

physics.bio-ph↗

arXiv2024

Adaptive Exponential Integrate-and-Fire Model with Fractal Extension

The description of neuronal activity has been of great importance in neuroscience. In this field, mathematical models are useful to describe the electrophysical behaviour of neurons. One successful model used for this purpose is the Adaptive Exponential Integrate-and-Fire (Adex), which is composed of two ordinary differential equations. Usually, this model is considered in his standard formulation, i.e., with integer order derivatives. In this work, we propose and study the fractal extension of Adex model, which in simple terms corresponds to replacing the integer derivative by non-integer. As non-integer operators, we choose the fractal derivatives. We explore the effects of equal and different orders of fractal derivatives in the firing patterns and mean frequency of the neuron described by the Adex model. Previous results suggest that fractal derivatives can provide a more realistic representation due to the fact that the standard operators are generalized. Our findings show that the fractal order influences the inter-spike intervals and changes the mean firing frequency. In addition, the firing patterns depend not only on the neuronal parameters but also on the order of respective fractal operators. As our main conclusion, the fractal order below the unit value increases the influence of the adaptation mechanism in the spike firing patterns.

physics.bio-ph↗

arXiv2023

Multistability and chaos in SEIRS epidemic model with a periodic time-dependent transmission rate

In this work, we study the dynamics of a SEIRS epidemic model with a periodic time-dependent transmission rate. Emphasizing the influence of the seasonality frequency on the system dynamics, we analyze the largest Lyapunov exponent along parameter planes finding large chaotic regions. Furthermore, in some ranges there are shrimp-like periodic strutures. We highlight the system multistability, identifying the coexistence of periodic orbits for the same parameter values, with the infections maximum distinguishing by up one order of magnitude, depending only on the initial conditions. In this case, the basins of attraction has self-similarity. Parametric configurations, for which both periodic and non-periodic orbits occur, cover $13.20\%$ of the evaluated range. We also identified the coexistence of periodic and chaotic attractors with different maxima of infectious cases, where the periodic scenario peak reaching approximately $50\%$ higher than the chaotic one.

physics.bio-ph↗

arXiv2023

Fractal and Fractional SIS model for syphilis data

This work studies the SIS model extended by fractional and fractal derivatives. We obtain explicit solutions for the standard and fractal formulations; for the fractional case, we study numerical solutions. As a real data example, we consider the Brazilian syphilis data from 2011 to 2021. We fit the data by considering the three variations of the model. Our fit suggests a recovery period of 11.6 days and a reproduction ratio ($R_0$) equal to 6.5. By calculating the correlation coefficient ($r$) between the real data and the theoretical points, our results suggest that the fractal model presents a higher $r$ compared to the standard or fractional case. The fractal formulation is improved when two different fractal orders with distinguishing weights are considered. This modification in the model provides a better description of the data and improves the correlation coefficient.

physics.bio-ph↗

arXiv2023

Fractional dynamics and recurrence analysis in cancer model

In this work, we analyze the effects of fractional derivatives in the chaotic dynamics of a cancer model. We begin by studying the dynamics of a standard model, {\it i.e.}, with integer derivatives. We study the dynamical behavior by means of the bifurcation diagram, Lyapunov exponents, and recurrence quantification analysis (RQA), such as the recurrence rate (RR), the determinism (DET), and the recurrence time entropy (RTE). We find a high correlation coefficient between the Lyapunov exponents and RTE. Our simulations suggest that the tumor growth parameter ($ρ_1$) is associated with a chaotic regime. Our results suggest a high correlation between the largest Lyapunov exponents and RTE. After understanding the dynamics of the model in the standard formulation, we extend our results by considering fractional operators. We fix the parameters in the chaotic regime and investigate the effects of the fractional order. We demonstrate how fractional dynamics can be properly characterized using RQA measures, which offer the advantage of not requiring knowledge of the fractional Jacobian matrix. We find that the chaotic motion is suppressed as $α$ decreases, and the system becomes periodic for $α\lessapprox 0.9966$. We observe limit cycles for $α\in (0.9966,0.899)$ and fixed points for $α<0.899$. The fixed point is determined analytically for the considered parameters. Finally, we discover that these dynamics are separated by an exponential relationship between $α$ and $ρ_1$. Also, the transition depends on a supper transient which obeys the same relationship.

physics.bio-ph↗

arXiv2022

Unpredictability in seasonal infectious diseases spread

In this work, we study the unpredictability of seasonal infectious diseases considering a SEIRS model with seasonal forcing. To investigate the dynamical behaviour, we compute bifurcation diagrams type hysteresis and their respective Lyapunov exponents. Our results from bifurcations and the largest Lyapunov exponent show bistable dynamics for all the parameters of the model. Choosing the inverse of latent period as control parameter, over 70% of the interval comprises the coexistence of periodic and chaotic attractors, bistable dynamics. Despite the competition between these attractors, the chaotic ones are preferred. The bistability occurs in two wide regions. One of these regions is limited by periodic attractors, while periodic and chaotic attractors bound the other. As the boundary of the second bistable region is composed of periodic and chaotic attractors, it is possible to interpret these critical points as tipping points. In other words, depending on the latent period, a periodic attractor (predictability) can evolve to a chaotic attractor (unpredictability). Therefore, we show that unpredictability is associated with bistable dynamics preferably chaotic, and, furthermore, there is a tipping point associated with unpredictable dynamics.

physics.soc-ph↗

arXiv2022

Effect of two vaccine doses in the SEIR epidemic model using a stochastic cellular automaton

In this work, to support decision making of immunisation strategies, we propose the inclusion of two vaccination doses in the SEIR model considering a stochastic cellular automaton. We analyse three different scenarios of vaccination: $i) unlimited doses, (ii) limited doses into susceptible individuals, and (iii) limited doses randomly distributed overall individuals. Our results suggest that the number of vaccinations and time to start the vaccination is more relevant than the vaccine efficacy, delay between the first and second doses, and delay between vaccinated groups. The scenario (i) shows that the solution can converge early to a disease-free equilibrium for a fraction of individuals vaccinated with the first dose. In the scenario (ii), few two vaccination doses divided into a small number of applications reduce the number of infected people more than into many applications. In addition, there is a low waste of doses for the first application and an increase of the waste in the second dose. The scenario (iii) presents an increase in the waste of doses from the first to second applications more than the scenario $(ii)$. In the scenario (iii), the total of wasted doses increases linearly with the number of applications. Furthermore, the number of effective doses in the application of consecutive groups decays exponentially overtime.

nlin.CG↗