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

Structural connectivity modifications in the brain of selected patients with tumour after its removal by surgery (a case study)

Acknowledgments This study was possible by partial financial support from the following agencies: Funda¸c˜ao Arauc´aria, Brazilian National Council for Scientific and Technological Development (CNPq), and Coordination for the Improvement of Higher Education Personnel (CAPES). S˜ao Paulo Research Foundation (FAPESP 2018/03211-6, 2022/13761-9). We thank 105 Group Science (www.105groupscience.com).Peer reviewe

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

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 ($\rho_1$) 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 $\alpha$ decreases, and the system becomes periodic for $\alpha \lessapprox 0.9966$. We observe limit cycles for $\alpha \in (0.9966,0.899)$ and fixed points for $\alpha<0.899$. The fixed point is determined analytically for the considered parameters. Finally, we discover that these dynamics are separated by an exponential relationship between $\alpha$ and $\rho_1$. Also, the transition depends on a supper transient which obeys the same relationship

Effects of drug resistance in the tumour-immune system with chemotherapy treatment

Acknowledgement This study was possible by partial financial support from the following Brazilian government agencies: Fundaao Araucaria, National Council for Scientific and Technological Development, Coordination for the Improvement of Higher Education Personnel, and Sao Paulo Research Foundation (2015/07311-7, 2017/18977- 1, 2018/03211-6, 2020/04624-2)Peer reviewedPostprin

Applications of Computer Technology in Complex Craniofacial Reconstruction

Background:. To demonstrate our use of advanced 3-dimensional (3D) computer technology in the analysis, virtual surgical planning (VSP), 3D modeling (3DM), and treatment of complex congenital and acquired craniofacial deformities. Methods:. We present a series of craniofacial defects treated at a tertiary craniofacial referral center utilizing state-of-the-art 3D computer technology. All patients treated at our center using computer-assisted VSP, prefabricated custom-designed 3DMs, and/or 3D printed custom implants (3DPCI) in the reconstruction of craniofacial defects were included in this analysis. Results:. We describe the use of 3D computer technology to precisely analyze, plan, and reconstruct 31 craniofacial deformities/syndromes caused by: Pierre-Robin (7), Treacher Collins (5), Apert’s (2), Pfeiffer (2), Crouzon (1) Syndromes, craniosynostosis (6), hemifacial microsomia (2), micrognathia (2), multiple facial clefts (1), and trauma (3). In select cases where the available bone was insufficient for skeletal reconstruction, 3DPCIs were fabricated using 3D printing. We used VSP in 30, 3DMs in all 31, distraction osteogenesis in 16, and 3DPCIs in 13 cases. Utilizing these technologies, the above complex craniofacial defects were corrected without significant complications and with excellent aesthetic results. Conclusion:. Modern 3D technology allows the surgeon to better analyze complex craniofacial deformities, precisely plan surgical correction with computer simulation of results, customize osteotomies, plan distractions, and print 3DPCI, as needed. The use of advanced 3D computer technology can be applied safely and potentially improve aesthetic and functional outcomes after complex craniofacial reconstruction. These techniques warrant further study and may be reproducible in various centers of care

Anomalous Relaxation and Three-Level System: A Fractional Schrödinger Equation Approach

We investigate a three-level system in the context of the fractional Schrödinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet. We first consider the three-level system omitting the kinetic term, i.e., taking into account only the transition among the levels, to analyze the effect of the fractional time derivative. Afterward, we incorporate a kinetic term and the fractional derivative in space to analyze simultaneous wave packet transition and spreading among the levels. For these cases, we obtain analytical and numerical solutions. Our results show a wide variety of behaviors connected to the fractional operators, such as the non-conservation of probability and the anomalous spread of the wave packet

Dynamics of a perturbed random neuronal network with burst-timing-dependent plasticity

Neuroplasticity, also known as brain plasticity or neuronal plasticity, allows the brain to improve its connections or rewire itself. The synaptic modifications can help the brain to enhance fitness, to promote existing cognitive capabilities, and to recover from some brain injuries. Furthermore, brain plasticity has impacts on neuronal synchronisation. In this work, we build a neuronal network composed of coupled Rulkov neurons with excitatory connections randomly distributed. We consider burst-timing-dependent plasticity to investigate the effects of external perturbations, such as periodic and random pulses, on the neuronal synchronous behaviour. The plasticity changes the synaptic weights between the presynaptic and postsynaptic neurons, and as a consequence the burst synchronisation. We verify that the external periodic and random pulsed perturbations can induce synchronisation and desynchronisation states. One of our main results is to demonstrate that bursting synchronisation and desynchronisation in a network with burst-timing-dependent plasticity can emerge according to alterations of the initial synaptic weights. Furthermore, we show that external periodic and random pulsed currents can be an effective method to suppress neuronal activities related to pathological synchronous behaviour

Fractional Diffusion Equation under Singular and Non-Singular Kernel and Its Stability

The fractional reaction–diffusion equation has been used in many real-world applications in fields such as physics, biology, and chemistry. Motivated by the huge application of fractional reaction–diffusion, we propose a numerical scheme to solve the fractional reaction–diffusion equation under different kernels. Our method can be particularly employed for singular and non-singular kernels, such as the Riemann–Liouville, Caputo, Fabrizio–Caputo, and Atangana–Baleanu operators. Moreover, we obtained general inequalities that guarantee that the stability condition depends explicitly on the kernel. As an implementation of the method, we numerically solved the diffusion equation under the power-law and exponential kernels. For the power-law kernel, we solved by considering fractional time, space, and both operators. In another example, we considered the exponential kernel acting on the time derivative and compared the numerical results with the analytical ones. Our results showed that the numerical procedure developed in this work can be employed to solve fractional differential equations considering different kernels