Nonlinear Dynamics

In this research, we create a new fractional-order SEIHRD framework to examine how the Nipah virus moves from one species to another (zoonotic spillover) and how it later spreads throughout a community (via contact with one another) or in a hospital or isolation situation (via entering into a hospital or being placed under quarantine). We used the fractional-derivative formulation of the SEIHRD model to demonstrate memory-based effects related to the progression of an infection and also reflect time-distributed effects associated with surveillance and control measures placed on an infected patient. We first demonstrated that the basic epidemiologic properties of the model were consistent by showing that the solutions of the SEIHRD differential equations will always yield positive and bounded solutions within biologically relevant parameter ranges. We then established the well-posedness of this model by transforming the SEIHRD differential equations into an equivalent integral operator and applying various fixed-point arguments to demonstrate that there will always be unique solution(s) to the SEIHRD differential equations. To evaluate the threshold parameter for the transmission of Nipah virus within a given population we calculated the threshold level through the next generation method to determine the expected number of secondary infections from a new or chronically infected host. One of the main contributions of this work is to include an analysis of the robustness of a given solution to all potential perturbations (i.e., Ulam-Hyers and generalized Ulam-Hyers stability). In addition, we provide analytic results guaranteeing that small perturbations due to approximate modeling, numerical approximation (discretization), or the lack of data fidelity will produce controlled deviations in the solutions. To finish this project, we perform a global sensitivity analysis on uncertain coefficients to evaluate their contribution to the uncertainty of each coefficient and to find out the coefficients that most strongly influence major outcome metrics. This will allow us to develop a priority order for prioritizing spillover control (reduction of human contact and/or isolation), contact reduction, and expenditure of resources towards isolation-related interventions. The resulting framework converts fractional epidemic modeling from a descriptive simulation to a replicable method with robustly defined behavior and equal response prediction.

Alzheimers disease (AD) is a devastating neurodegenerative disease whose etiology is poorly understood and for which current treatments provide only modest control of symptoms. To better investigate the causes and progression of the disease, the transgenic TgF344-AD rat model has emerged as a crucial tool. In this paper, we collect observations on the accumulation of amyloid-{beta}, changes in neuronal density, and a decline in cognitive performance in TgF344-AD and wild-type rats. We develop a compartmental ordinary differential equation model and determine its parameters by fitting the output to the experimental observations. Our model simulations support the hypothesis that the accumulation of amyloid-{beta} leads to a rapid decline in neuronal density followed by a significant loss in memory and learning ability. Our mathematical model can provide a bridge between AD research in rodent models and the human condition of AD.

This study presents a theoretical and mathematical framework for understanding the dynamical behavior of infectious disease spread using a compartmental modeling approach. The proposed model incorporates memory effects to capture temporal dependencies that are not adequately represented by classical formulations. Qualitative analysis is employed to investigate the stability properties of the system and the role of key mechanisms in shaping long term dynamics. Publicly available surveillance information is used only to illustrate the consistency of the model behavior with observed trends. The results highlight the value of memory based modeling structures for describing complex biological processes and provide a general mathematical perspective for studying epidemic dynamics.

Voltage perturbations to a repetitively firing Hodgkin-Huxley (HH) model of neuronal spiking in the bistable regime with coexisting limit cycle and stable steady node can either lead to the spikes phase resetting or collapse to the stable steady state. The latter describes a non-firing hyperpolarized quiescent state of the neuron despite the presence of constant external current. Using asymptotic phase response curve (PRC), the impact of voltage perturbations on a repetitively firing HH model is studied here while it is diffusively coupled to another HH model under identical external stimulation. It is observed that the pre-perturbation state of synchronization and the coupling strength critically determine the PRC response of the perturbed HH dynamics. Higher coupling strengths of perfectly in-phase (anti-phase) synchronized HH models shrink (expand) the combinatorial space of perturbation strengths and the oscillation phases causing collapse to the quiescent state. This indicates reduced (enlarged) basin of attraction, viz. the null space, associated with the steady state in the HH phase space. The findings bear important implications to the spiking dynamics of diverse interneurons, as well as special cases of pyramidal neurons, coupled through electrical synapses via. gap junctions, and suggest the role of gap junction plasticity in tuning vulnerability to quiescent state in the presence of biological noise and spikelets.

Mass-conserved reaction-diffusion systems are used as mathematical models for various phenomena such as cell polarity. Numerical simulations of this system present transient dynamics in which multiple stripe patterns converge to spatially monotonic patterns. Previous studies indicated that the transient dynamics are driven by a mass conservation law and by variations in the amount of substance contained in each pattern, which we refer to as "pattern flux". However, it is challenging to mathematically investigate these pattern dynamics. In this study, we introduce a reaction-diffusion compartment model to investigate the pattern dynamics in view of the conservation law and the pattern flux. This model is defined on multiple intervals (compartments), and diffusive couplings are imposed on each boundary of the compartments. Corresponding to the transient dynamics in the original system, we consider the dynamics around stripe patterns in the compartment model. We derive ordinary differential equations describing the pattern dynamics of the compartment model and analyze the existence and stability of equilibria for the reduced ODE with respect to the boundary parameters. For a specific parameter setting, we obtained results consistent with previous studies. Moreover, we present that the stripe patterns in the compartment model are potentially stabilized by changing the parameter, which is not observed in the original system. We expect that the methodology developed in this paper is extendable to various directions, such as membrane-induced pattern control.

BackgroundTo control leishmaniasis, chemotherapy drugs are currently under development. However, these drugs often exhibit poor efficacy and are associated with toxicity, adverse effects, and drug resistance. At present, no specific drug is available for the treatment of leishmaniasis. Meanwhile, vaccine research is ongoing. Recent studies have analysed some experimental vaccines using mathematical models. AimIn previous work, drug targeting was focused on the entire human body rather than specifically addressing infected macrophages and parasites. In our current approach, we aim to eliminate infected macrophages and parasites through nano-drug design. Specifically, we utilise two types of nanoparticles: iron oxide and citric acid-coated iron oxide. Moving forward, we plan to advance this strategy using mathematical modelling of macrophage-parasite interactions. MethodsWe design PDE-based models of macrophages and parasites, incorporating cytokine dynamics, to support nano-drug development. Drug efficacy is estimated using posterior distributions to analyse phenotypic fluctuations of macrophages and parasites during the design phase. We investigate implicit and semi-implicit treatment schemes, focusing on energy decay properties. To model drug flow during treatment, we introduce a three-phase moving boundary problem. Comparative analyses are conducted to evaluate macrophage and parasite behaviour with and without treatment. Finally, the entire framework is implemented within a virtual lab environment. ResultsThe results show that the nano-drug exhibits better efficacy compared to combined drug doses. We analysed and compared two types of nano-drug particles: iron oxide and citric acid-coated iron oxide. We discuss how the drug effectively targets and eliminates infected macrophages and parasites. ConclusionOur models results and simulations will support researchers conducting further studies in nano-drug design for leishmaniasis. These simulations are performed within a virtual lab environment.

Following the suggestion of L. F. Jaffe [1] we propose a mathematical model of fast calcium induced calcium influx waves (CICI Waves). They can propagate at relatively high speeds (up to 1300 micrometers/s). According to [1], they propagate due to a mechanochemical interaction of actomyosin network with the cell membrane. The local stretching of the membrane caused by actin filaments opens mechanically operated ion channels resulting in the influx of calcium to the cell. Moreover, stretching a cells membrane at one point opens nearby stretch activated calcium channels because the mechanical force is relayed by the actin filaments interconnected by myosin bridges. The number of bridges as well as filament density increases with calcium concentration, causing the contraction of the actomyosin network. Thus, the force acting on the membrane from tangled actin filaments is transmitted ahead of the moving front of the calcium concentration. As a result, the ion channels are opened even before the signal of calcium reaches them. This leads to much larger propagation speed of CICI waves in comparison with calcium induced calcium released (CICR) waves, where the wave is sustained by the diffusion of calcium and autocatalytic release of calcium from the internal stores (e.g. endoplasmic reticula).

The COVID-19 pandemic has presented severe challenges in understanding and predicting the spread of infectious diseases, necessitating innovative approaches beyond traditional epidemiological models. This study introduces an advanced method for automated model discovery using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, leveraging a dataset from the COVID-19 outbreak in Thuringia, Germany, encompassing over 400,000 patient records and vaccination data. By analysing this dataset, we develop a flexible, data-driven model that captures many aspects of the complex dynamics of the pandemics spread. Our approach incorporates external factors and interventions into the mathematical framework, leading to more accurate modelling of the pandemics behaviour. The fixed coefficient values of the differential equation as globally determined by the SINDy were not found to be accurate for locally modelling the measured data. We therefore refined our technique based on the differential equations as found by SINDy, by investigating three modifications that account for recent local data. In a first approach, we re-optimized the coefficient values using seven days of past data, without changing the globally determined differential equation. In a second approach, we allowed a temporal dependence of the coefficient values fitted using all previous data in combination with regularization. As a last method, we kept the coefficients fixed to the original values but augmented the differential equation with a small neural network, locally optimized to the data of the past week. Our findings reveal the critical role of vaccination and public health measures in the pandemics trajectory. The proposed model offers a robust tool for policymakers and health professionals to mitigate future outbreaks, providing insights into the efficacy of intervention strategies and vaccination campaigns. This study advances the understanding of COVID-19 dynamics and lays the groundwork for future research in epidemic modelling, emphasising the importance of adaptive, data-informed approaches in public health planning.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity.

Age related macular degeneration is known to be one of the major causes of irreversible blindness among the older generation. We present a mathematical model of partial differential equations for the therapy of this disease, which is based on the intravitreal injection of a drug into the vitreous body. For the treatment to work, the drug has to travel past the inner-limiting membrane into the retina and reduce the free vascular endothelial growth factor (VEGF) concentration by binding to at least one of the two binding sites of the VEGF molecule. Therefore, our model consists of two compartments, the vitreous and the retina. In the vitreous we employ four coupled convection-diffusion-reaction equations with an additional coupling to the underlying aqueous humor flow and four coupled diffusion-reaction equations in the retina. The resulting PDE system is solved numerically in a realistic 3D eye geometry. Temporal discretization is based on one-step theta schemes and spatial discretization is done using the Finite Element method. The numerical results are used to demonstrate the therapy concept and to analyze the drug efficacy of aflibercept and ranibizumab. The results show, among other things, that only about 20 % of the drug reaches the retina through the inner-limiting membrane and that 50 % of the VEGF concentration has been rebuilt in the retina after 38.19 days for a single ranibizumab injection.

A key component of intraneuronal communication is the modulation of postsynaptic firing frequencies by stochastic transmitter release from presynaptic neurons. The time interval between successive postsynaptic firings is called the inter-spike interval (ISI), and understanding its statistics is integral to neural information processing. We start with a model of an excitatory chemical synapse with postsynaptic neuron firing governed as per a classical integrate-and-fire model. Using a first-passage time framework, we derive exact analytical results for the ISI statistical moments, revealing parameter regimes driving precision in postsynaptic action potential timing. Next, we extended this analysis to include both an excitatory and an inhibitory presynaptic connection onto the same postsynaptic neuron. We consider both a fixed postsynaptic-firing threshold and a threshold that adapts based on the postsynaptic membrane potential history. Our analysis shows that the latter adaptive threshold can result in scenarios where increasing the inhibitory input frequency increases the postsynaptic firing frequency. Moreover, we characterize parameter regimes where ISI noise is hypo-exponential or hyperexponential based on its coefficient of variation being less than or higher than one, respectively.

As social beings, humans make decisions partly based on social interaction. Observing the behavior of others can lead to learning from and about them, potentially increasing trust and prompting trust-based behavioral changes. Observation-based decision making involves different neural structures. The orbitofrontal cortex (OFC) and lateral prefrontal cortex (LPFC) are known as neural structures mainly involved in processing emotional and cognitive decision values, respectively, while the anterior cingulate cortex (ACC) plays a pivotal role as a social hub, integrating the afferent expectancy signals from OFC and LPFC. This paper presents a neurocomputational model of the interplay between observational learning and trust, as well as their role in individual decision-making. Our model elucidates and predicts the emotional and rational behavioral changes of an individual influenced by observing the action-outcome association of an alleged expert. We have modeled the neurodynamics of three cortical structures (OFC, LPFC, and ACC) and their interactions, where the neural oscillatory properties, modeled with Dynamic Bayesian Probability, represent the observers attitude towards the expert and the decision options. As an example of an everyday behavioral situation related to climate change, we use the choice of transportation between home and work. The EEG-like simulation outputs from our model represent the presumed brain activity of an individual making such a choice, assuming the decision-maker is exposed to social information.

A field trial was conducted using 10% lambda-cyhalothrin microcapsule suspension to provide a method for killing ticks and preventing diseases in outdoor gatherings of people or temporary resettlement places after disasters. In this study, three field experimental sites were selected, and each experimental site was set up with a test area and a control area. Before pesticide application, the tick density in three test areas and three control areas was surveyed using the flagging method. Subsequently, two methods were used for pesticide spraying: motorized fogging and electric constant-volume spraying (with the pesticide diluted 300 times). The relative density decline rate of ticks was calculated in three test sites on days 1, 7, 14, 21, and 28 after spraying, and all experimental areas achieved good tick-killing effects. Even without prohibiting wild animals, grazing sheep, and dogs (which are often infested with ticks and not treated) from entering the trial sites, spraying 10% lambda-cyhalothrin microcapsule suspension could maintain a tick-free (low-density) state for approximately 3-4 weeks. Our study provides an idea for controlling epidemics through tick elimination during the high incidence period of tick-borne diseases.

With significant population fractions in many societies who refuse vaccines, it is important to reconsider how vaccination is incorporated into compartmental epidemiology models. It is still most common to apply the vaccination rate to the entire class of susceptibles, rather than to use the more realistic assumption that the vaccination rate function should depend only on the population of susceptibles who are willing and able to receive a vaccination. This study uses a simple generic disease model to address two questions: (1) How much error is introduced in key model outcomes by neglecting vaccine unwillingness?, and (2) Can the error be reduced by incorporating vaccine unwillingness into the vaccination rate constant rather than the rate diagram? The answers depend greatly on the time scale of interest. For the endemic time scale, where longterm behavior is studied with equilibrium point analysis, the error in neglecting unwillingess is large and cannot be improved upon by decreasing the vaccination rate constant. For the epidemic time scale, where the first big epidemic wave is studied with numerical simulations, the error can still be significant, particularly for diseases that are relatively less infectious and vaccination programs that are relatively slow.

Visceral leishmaniasis (VL) is considerably more severe among individuals infected with human immunodeficiency virus (HIV), leading to higher parasite loads, frequent relapse, and increased mortality. To examine the epidemiological interaction between the two diseases, we develop a comprehensive VL-HIV co-infection model that incorporates transmission pathways, treatment effects, and relapse dynamics. The model is parameterized using real-time data from Bihar, India, including monthly VL-only and VL-HIV co-infected cases and annual HIV prevalence data. Our analysis shows that HIV infection drives the resurgence and persistence of VL even in settings where VL alone would not sustain transmission, underscoring the amplifying effect of HIV-induced immunosuppression on VL dynamics. We further demonstrate that increasing HIV treatment coverage substantially reduces co-infection prevalence and lowers VL relapse rates. Numerical simulations and optimal control analysis highlight the effectiveness of integrated intervention strategies that combine awareness, treatment enhancement, and vector control. Overall, this study emphasizes the need for coordinated VL and HIV control programs and provides data-driven guidance for designing sustainable intervention strategies in endemic regions.

Monkeypox viral disease has been and continues to be a global public health concern. Currently, there are existing, though minimal measures to manage mpox and any future outbreaks. Relying on data-driven modeling for early detection of mpox and prediction of possible cases and deaths in the presence of an outbreak is thus imperative. The present study forecasted global mpox virus cases and deaths in Asia, Africa, Australia, Europe, North America, Oceania, and South America. Three forecasting models (deep neural network, gradient boosting, and polynomial regression) were trained on data from the seven geographical regions. The performance of the three models was assessed using coefficient of determination, mean squared error, root mean squared error, and mean absolute scaled error across each region. Prediction using the deep neural network revealed a potential of higher mpox deaths in Africa and higher mpox cases in South America. Prediction using gradient boosting showed a potential of mpox deaths in Africa and higher mpox cases in Asia and North America. Prediction using polynomial regression revealed a potential of higher mpox deaths in Africa and Asia while rapid rises in mpox cases from 2025 to 2028 were anticipated in all regions except Asia in case of a monkeypox outbreak. For the three models, the tree-based ML model (gradient boosting) outperformed the statistical model and deep learning model by R2 and MSE in predicting mpox case counts across all the seven geographical regions. This study showcases the worth in using data-driven modelling to predict emerging and re-emerging infectious diseases such as mpox.

Hippocampus is known to replay activity patterns to recall and process memories, which is often related to Hopfield-type attractor dynamics. Another line of theoretical studies suggests that hippocampal replay prioritizes replay of experiences to accelerate value learning for efficient decision making. It is unknown how hippocampal attractor dynamics perform prioritized memory sampling, and more broadly, how we can consistently relate dynamical (bottom-up) and functional (top-down) theories of hippocampal replay. In this paper, we propose an extended Hopfield-type attractor network model with momentum, kinetic energy, and conservation of the total energy, which is called momentum Hopfield model. We show that our model can be interpreted as CA3-CA1 network model with intrinsic oscillation, and such network model reproduces hippocampal replay in 1-D and 2-D spatial structures. We also prove that our model functionally works as Markov-chain Monte Carlo sampling in which recall frequencies of memory patterns can be arbitrarily biased. Using this property, we implemented prioritized experience replay using our model, which actually accelerated reinforcement learning for spatial navigation. Our model explains how dynamics of hippocampal circuits realize efficient memory sampling, providing a theoretical link between dynamics and functions of hippocampal replay.

Vaccine-acquired immunity plays an important role in controlling the spread of many infectious diseases; however, vaccine efficacy can diminish over time. This work uses a mathematical model to study the effects of waning vaccination-acquired immunity on infection incidence. With an SEIR-type compartmental model that considers both vaccinated and unvaccinated populations (and their mixing), we present mathematical conditions under which vaccinated individuals drive ongoing growth in infections, i.e., over half of the daily incidence arises from vaccinated individuals. Analysis of a mathematical model of COVID-19 spread in the state of Colorado suggests how and for what duration vaccinated individuals could have sustained such growth. Importantly, our model demonstrates that, despite potential for brief vaccinated-driven periods of growth in infections, which occur among unvaccinated-driven periods of growth in infections, increased vaccination coverage always reduces total cases and total hospitalizations. This work provides insight into how waning immunity in vaccinated populations can contribute to ongoing infection incidence and demonstrates the value of complementary interventions to prevent disease spread in vaccinated populations.

ObjectiveHyperhomocysteinemia (HHcy) affects approximately 75% of the population in China, and there is currently controversy regarding whether HHcy increases the risk of hemorrhagic stroke. This study aims to investigate the effects of high homocysteine (Hcy) levels on cerebral hemorrhage in hypertensive mice by administering homocysteine to them. MethodsMale C57BL/6 mice at 8 months of age were used in the experiment. The study was divided into two groups: the Hcy + AngII + L - NAME group and the AngII + L - NAME group. Magnetic resonance imaging (MRI) was performed when the mice exhibited signs of cerebral hemorrhage.After the hemorrhage, anesthesia was induced to euthanize the animals, and then the brain tissue was fixed. The total rearing period was 18 weeks. The relationship between homocysteine and stroke was described by plotting survival curves. The location and quantity of cerebral hemorrhage were determined through histopathological staining. ResultsThe serum Hcy concentration of mice fed with Hcy for 6 weeks increased to 23.07 mol/L, and the blood pressure ranged from 170 to 180 mmHg. The number of deaths due to cerebral hemorrhage was 10 in both the AngII + L - NAME + Hcy group and the AngII + L - NAME group. The p - value of the survival curves between the two groups was 0.162, indicating no statistically significant difference. ConclusionThe results demonstrated that elevated homocysteine levels did not influence the incidence of intracerebral hemorrhage in hypertensive mice. Hyperhomocysteinemia does not increase the risk of intracerebral hemorrhage in hypertensive mice

IntroductionClimate change is a global adverse phenomenon affecting the health and wellbeing of all humans, and timely awareness can help mitigate these health effects. ObjectiveTo understand the knowledge and attitudes of Sri Lankan adults towards climate change and its effects on human health. MethodsA web based cross-sectional survey was conducted using a structured, pretested, web based, self-administered questionnaire, using a respondent driven sampling technique, among Sri Lankan adults. Data was collected over three months, from 1st September 2022. Responses were automatically stored in a cloud-based database and were imported into a spreadsheet and analysed using MS Excel. ResultsMajority of the 118 respondents were young, educated, employed adults from western province, and 56.78% were females. Overall knowledge on climate change was good among 82.20%, while over 90% had a good or favourable knowledge on health effects associated with climate change. Respondents demonstrated a good awareness of climate effects on skin cancer (92.37%), mental illnesses (82.2%) and asthma (82.2%), but were less aware of the effects on diabetes (28.8%), COPD (38.1%) and heart diseases (46.6%), and vector borne diseases such as Malaria (57.6%) and Dengue (61.8%). Over 90% had a good attitude towards the need for climate change mitigation and climate friendly activities being implemented. ConclusionsUrban, educated Sri Lankan adults had a good understanding and awareness on the health effects of climate change, and the importance of mitigating it in relation to its health effects, but further studies are needed to understand the awareness levels of the less educated rural communities.