A global report on the dynamics of COVID-19 with quarantine and hospitalization: A fractional order model with non-local kernel

Synergistic modeling of hemorrhagic dengue fever: Passive immunity dynamics and time-delay neural network analysis

Dengue fever poses a formidable epidemiological challenge, particularly for vulnerable groups such as infants. This research paper establishes a mathematical model to describe the dynamics of secondary immunity in infants against dengue hemorrhagic fever, who acquired primary immunity through maternal antibodies. The effect of passive immunity in the form of dengue immunoglobulin is analyzed for high-risk patients for different scenarios, including standard dengue infections, host with pre-existing immunity, delayed diagnosis or treatment, and end-stage dengue cases. Convergence analysis of the model is performed through disease free and disease endemic equilibrium points in terms of basic reproduction number R0 along with local stability of disease-free equilibrium point. Adams numerical approach is utilized to simulate dengue disease/immunity interactions. A time delay exogenous neural network approach coupled with Levenberg-Marquardt optimization is designed to characterize, model and simulate these curated scenarios. Exhaustive neural network procedures determine the efficacy of the neural network approach by means of mean square error (MSE) loss charts, error correlation graphs, error histogram analysis and time-series prediction charts. The impeccable characterization of the dengue fever scenarios is supported by extremely low MSE results of the order 10-9 to 10-11. To further showcase the competency of the neural network predictions, an exhaustive comparative study against the reference numerical solutions is illustrated with absolute errors in the range of 10-3 to 10-5. The novel development of mathematical model coupled with time-delay exogenous neural networks significantly enhances our ability to understand and predict the intricate dengue hemorrhagic fever dynamics allowing for targeted interventions for such infectious disease and epidemiological scenarios.

Exploring optimal control strategies in a nonlinear fractional bi-susceptible model for Covid-19 dynamics using Atangana-Baleanu derivative

In this article, a nonlinear fractional bi-susceptible [Formula: see text] model is developed to mathematically study the deadly Coronavirus disease (Covid-19), employing the Atangana-Baleanu derivative in Caputo sense (ABC). A more profound comprehension of the system's intricate dynamics using fractional-order derivative is explored as the primary focus of constructing this model. The fundamental properties such as positivity and boundedness, of an epidemic model have been proven, ensuring that the model accurately reflects the realistic behavior of disease spread within a population. The asymptotic stabilities of the dynamical system at its two main equilibrium states are determined by the essential conditions imposed on the threshold parameter. The analytical results acquired are validated and the significance of the ABC fractional derivative is highlighted by employing a recently proposed Toufik-Atangana numerical technique. A quantitative analysis of the model is conducted by adjusting vaccination and hospitalization rates using constant control techniques. It is suggested by numerical experiments that the Covid-19 pandemic elimination can be expedited by adopting both control measures with appropriate awareness. The model parameters with the highest sensitivity are identified by performing a sensitivity analysis. An optimal control problem is formulated, accompanied by the corresponding Pontryagin-type optimality conditions, aiming to ascertain the most efficient time-dependent controls for susceptible and infected individuals. The effectiveness and efficiency of optimally designed control strategies are showcased through numerical simulations conducted before and after the optimization process. These simulations illustrate the effectiveness of these control strategies in mitigating both financial expenses and infection rates. The novelty of the current study is attributed to the application of the structure-preserving Toufik-Atangana numerical scheme, utilized in a backward-in-time manner, to comprehensively analyze the optimally designed model. Overall, the study's merit is found in its comprehensive approach to modeling, analysis, and control of the Covid-19 pandemic, incorporating advanced mathematical techniques and practical implications for disease management.

A novel radial basis neural network for the Zika virus spreading model

The motive of current investigations is to design a novel radial basis neural network stochastic structure to present the numerical representations of the Zika virus spreading model (ZVSM). The mathematical ZVSM is categorized into humans and vectors based on the susceptible S(q), exposed E(q), infected I(q) and recovered R(q), i.e., SEIR. The stochastic performances are designed using the radial basis activation function, feed forward neural network, twenty-two numbers of neurons along with the optimization of Bayesian regularization in order to solve the ZVSM. A dataset is achieved using the explicit Runge-Kutta scheme, which is used to reduce the mean square error (MSE) based on the process of training for solving the nonlinear ZVSM. The division of the data is categorized into training, which is taken as 78 %, while 11 % for both authentication and testing. Three different cases of the nonlinear ZVSM have been taken, while the scheme's correctness is performed through the matching of the results. Furthermore, the reliability of the scheme is observed by applying different performances of regression, MSE, error histograms and state transition.

K1K2NN: A novel multi-label classification approach based on neighbors for predicting COVID-19 drug side effects

COVID-19, a novel ailment, has received comparatively fewer drugs for its treatment. Side Effects (SE) of a COVID-19 drug could cause long-term health issues. Hence, SE prediction is essential in COVID-19 drug development. Efficient models are also needed to predict COVID-19 drug SE since most existing research has proposed many classifiers to predict SE for diseases other than COVID-19. This work proposes a novel classifier based on neighbors named K1 K2 Nearest Neighbors (K1K2NN) to predict the SE of the COVID-19 drug from 17 molecules' descriptors and the chemical 1D structure of the drugs. The model is implemented based on the proposition that chemically similar drugs may be assigned similar drug SE, and co-occurring SE may be assigned to chemically similar drugs. The K1K2NN model chooses the first K1 neighbors to the test drug sample by calculating its similarity with the train drug samples. It then assigns the test sample with the SE label having the majority count on the SE labels of these K1 neighbor drugs obtained through a voting mechanism. The model then calculates the SE-SE similarity using the Jaccard similarity measure from the SE co-occurrence values. Finally, the model chooses the most similar K2 SE neighbors for those SE determined by the K1 neighbor drugs and assigns these SE to that test drug sample. The proposed K1K2NN model has showcased promising performance with the highest accuracy of 97.53% on chemical 1D drug structure and outperforms the state-of-the-art multi-label classifiers. In addition, we demonstrate the successful application of the proposed model on gene expression signature datasets, which aided in evaluating its performance and confirming its accuracy and robustness.

A stochastic approach for co-evolution process of virus and human immune system

Infectious diseases have long been a shaping force in human history, necessitating a comprehensive understanding of their dynamics. This study introduces a co-evolution model that integrates both epidemiological and evolutionary dynamics. Utilizing a system of differential equations, the model represents the interactions among susceptible, infected, and recovered populations for both ancestral and evolved viral strains. Methodologically rigorous, the model's existence and uniqueness have been verified, and it accommodates both deterministic and stochastic cases. A myriad of graphical techniques have been employed to elucidate the model's dynamics. Beyond its theoretical contributions, this model serves as a critical instrument for public health strategy, particularly predicting future outbreaks in scenarios where viral mutations compromise existing interventions.

On mathematical modelling of measles disease via collocation approach

Measles, a highly contagious viral disease, spreads primarily through respiratory droplets and can result in severe complications, often proving fatal, especially in children. In this article, we propose an algorithm to solve a system of fractional nonlinear equations that model the measles disease. We employ a fractional approach by using the Caputo operator and validate the model's by applying the Schauder and Banach fixed-point theory. The fractional derivatives, which constitute an essential part of the model can be treated precisely by using the Broyden and Haar wavelet collocation methods (HWCM). Furthermore, we evaluate the system's stability by implementing the Ulam-Hyers approach. The model takes into account multiple factors that influence virus transmission, and the HWCM offers an effective and precise solution for understanding insights into transmission dynamics through the use of fractional derivatives. We present the graphical results, which offer a comprehensive and invaluable perspective on how various parameters and fractional orders influence the behaviours of these compartments within the model. The study emphasizes the importance of modern techniques in understanding measles outbreaks, suggesting the methodology's applicability to various mathematical models. Simulations conducted by using MATLAB R2022a software demonstrate practical implementation, with the potential for extension to higher degrees with minor modifications. The simulation's findings clearly show the efficiency of the proposed approach and its application to further extend the field of mathematical modelling for infectious illnesses.

Equilibrium points and their stability of COVID-19 in US

This study aims to develop an advanced mathematic model and investigate when and how will the COVID-19 in the US be evolved to endemic. We employed a nonlinear ordinary differential equations-based model to simulate COVID-19 transmission dynamics, factoring in vaccination efforts. Multi-stability analysis was performed on daily new infection data from January 12, 2021 to December 12, 2022 across 50 states in the US. Key indices such as eigenvalues and the basic reproduction number were utilized to evaluate stability and investigate how the pandemic COVD-19 will evolve to endemic in the US. The transmissional, recovery, vaccination rates, vaccination effectiveness, eigenvalues and reproduction numbers ([Formula: see text] and [Formula: see text]) in the endemic equilibrium point were estimated. The stability attractor regions for these parameters were identified and ranked. Our multi-stability analysis revealed that while the endemic equilibrium points in the 50 states remain unstable, there is a significant trend towards stable endemicity in the US. The study's stability analysis, coupled with observed epidemiological waves in the US, suggested that the COVID-19 pandemic may not conclude with the virus's eradication. Nevertheless, the virus is gradually becoming endemic. Effectively strategizing vaccine distribution is pivotal for this transition.

Enhancing medical ultrasound imaging through fractional mathematical modeling of ultrasound bubble dynamics

The classical mathematical modeling of ultrasound acoustic bubble is so far using to improve the medical imaging quality. A clear and visible medical ultrasound image relies on bubble's diameter, wavelength and intensity of the scattered sound. A bubble with diameter much smaller than the sound wavelength is regarded as highly efficient source of sound scattering. The dynamical equation for a medical ultrasound bubble is primarily modeled in classical integer-order differential equation. Then a reduction of order technique is used to convert the modeled dynamic equation for the bubble surface into a system of incommensurate fractional-orders. The incommensurate fractional-order values are calculated directly, by using Riemann stability region. On the basis of stability the convergence and accuracy of the numerical scheme is also discussed in detail. It has been found that the system will remain stable and chaotic for the incommensurate values α1<0.737 and α2<2.80, respectively.

On the analysis of the fractional model of COVID-19 under the piecewise global operators

An expanding field of study that offers fresh and intriguing approaches to both mathematicians and biologists is the symbolic representation of mathematics. In relation to COVID-19, such a method might provide information to humanity for halting the spread of this epidemic, which has severely impacted people's quality of life. In this study, we examine a crucial COVID-19 model under a globalized piecewise fractional derivative in the context of Caputo and Atangana Baleanu fractional operators. The said model has been constructed in the format of two fractional operators, having a non-linear time-varying spreading rate, and composed of ten compartmental individuals: Susceptible, Infectious, Diagnosed, Ailing, Recognized, Infectious Real, Threatened, Recovered Diagnosed, Healed and Extinct populations. The qualitative analysis is developed for the proposed model along with the discussion of their dynamical behaviors. The stability of the approximate solution is tested by using the Ulam-Hyers stability approach. For the implementation of the given model in the sense of an approximate piecewise solution, the Newton Polynomial approximate solution technique is applied. The graphing results are with different additional fractional orders connected to COVID-19 disease, and the graphical representation is established for other piecewise fractional orders. By using comparisons of this nature between the graphed and analytical data, we are able to calculate the best-fit parameters for any arbitrary orders with a very low error rate. Additionally, many parameters' effects on the transmission of viral infections are examined and analyzed. Such a discussion will be more informative as it demonstrates the dynamics on various piecewise intervals.

Fractal fractional analysis of non linear electro osmotic flow with cadmium telluride nanoparticles

Numerical simulations of non-linear Casson nanofluid flow were carried out in a microchannel using the fractal-fractional flow model. The nano-liquid is prepared by dispersing Cadmium Telluride nanoparticles in common engine oil. Using relative constitutive equations, the system of mathematical governing equations has been formulated along with initial and boundary conditions. Dimensionless variables have been used to obtain the non-dimensional form of the governing equations. The fractal-fractional model has been obtained by employing the fractal-fractional operator of the exponential kernel. As the exact solution of the non-linear fractal-fractional model is very tough to find, therefore the formulated model has been solved numerically via the Crank-Nicolson scheme. Various plots are generated for the inserted parameters. From the analysis, it has been observed that a greater magnitude of the electro-kinetic parameter slows down the fluid's velocity. It is also worth noting that the fractional and classical models can also be derived from the fractal-fractional model by taking the parameters tend to zero. From the analysis, it is also observed that in response to 0.04 volume fraction of cadmium telluride nanoparticles, the rate of heat transfer (Nusselt number) and rate of mass transfer (Sherwood number) increased by 15.27% and 2.07% respectively.

Comparative Dynamics of Delta and Omicron SARS-CoV-2 Variants across and between California and Mexico

Evolutionary analysis using viral sequence data can elucidate the epidemiology of transmission. Using publicly available SARS-CoV-2 sequence and epidemiological data, we developed discrete phylogeographic models to interrogate the emergence and dispersal of the Delta and Omicron variants in 2021 between and across California and Mexico. External introductions of Delta and Omicron in the region peaked in early July (2021-07-10 [95% CI: 2021-04-20, 2021-11-01]) and mid-December (2021-12-15 [95% CI: 2021-11-14, 2022-01-09]), respectively, 3 months and 2 weeks after first detection. These repeated introductions coincided with domestic migration events with no evidence of a unique transmission hub. The spread of Omicron was most consistent with gravity centric patterns within Mexico. While cross-border events accounted for only 5.1% [95% CI: 4.3-6] of all Delta migration events, they accounted for 20.6% [95% CI: 12.4-29] of Omicron movements, paralleling the increase in international travel observed in late 2021. Our investigations of the Delta and Omicron epidemics in the California/Mexico region illustrate the complex interplay and the multiplicity of viral and structural factors that need to be considered to limit viral spread, even as vaccination is reducing disease burden. Understanding viral transmission patterns may help intra-governmental responses to viral epidemics.