Abstract The emergence and dynamic prevalence of genetic disorders and infectious diseases with mutations pose significant challenges for public health interventions. This study investigated the parameter estimation approach and the application of the dynamic state-space Markov modeling of these conditions. Using extensive simulations, the model demonstrated robust parameter estimation performance, with biases and mean-squared errors decreasing as sample size increased. Applying the model to COVID-19 data revealed distinct temporal patterns for each variant, highlighting their unique emergence, peak dominance, and decline or persistence trajectories. Despite the absence of clear trends in the data, the model exhibited a remarkable accuracy in predicting future prevalence trends for most variants, showcasing its potential for real-time monitoring and analysis. While some discrepancies were observed for specific variants, these findings suggest the model’s promise as a valuable tool for informing public health strategies. Further validation with larger datasets and exploration of incorporating additional factors hold the potential for enhancing the model’s generalizability and applicability to other evolving diseases.

Abstract Urbanization has been a growing trend for decades, but the Coronavirus disease 2019 (COVID-19) pandemic has accelerated this trend in several ways. In many countries, the pandemic has prompted significant investments in urban health infrastructure, including hospitals, clinics, and public health facilities. Also, there are many studies suggesting that COVID-19, urbanization, and chronic diseases are interconnected in several ways, and addressing one aspect requires a comprehensive approach that considers the interconnectedness of these factors. To date, there are no studies depicting COVID-19 as a cause of emerging chronic diseases within the urban population. To address this sensitive issue, we propose a mathematical model in which we divide the total human population into three compartments: susceptible, diseased, and recovered. We have obtained the equilibrium points of the model and the conditions for their local stabilities. A suitable Lyapunov function has been used to derive the condition for the global stability of the nontrivial equilibrium point. A detailed numerical simulation of the model has been carried out, which is followed by sensitivity analysis of the model system.

Abstract In this manuscript, we examine the blood alcohol model to investigate the dynamics of alcohol concentration in the human body. The classical model of blood alcohol concentration is converted into the fractional model by using Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu-Caputo derivatives. The existence and uniqueness theory for the model’s solution is constructed using the Banach fixed point theory. Also, the stability of the solution is established by Ulam-Hyers conditions. For the numerical simulation of the considered model, the Adams-Bashforth method with a two-step Lagrange polynomial is used and the numerical solution of the model with three different derivatives is presented in the tabular and graphical form. The comparison between the exact solution and observed solution is made by root mean square technique which is found to be in good agreement. Finally, the results from the three fractional derivatives are also compared with the exact data, which revealed that the CF fractional derivative performs better than the other two fractional derivatives.

Abstract In this work, we propose a hybrid impulsive prey-predator-mutualist model on nonuniform time domains. We have investigated the permanence/persistence results for the proposed model using the comparison theorems of impulsive differential equations and some dynamic inequality on the nonuniform time domains. In addition, we have established certain necessary requirements for the uniform asymptotic stability of the almost periodic solution and global attractivity of the proposed model. Furthermore, we provide several numerical examples on nonuniform time domains with computer simulation to demonstrate the viability of the results of the acquired analytical work.

Abstract As per the World Health Organization’s (WHO’s) suggestions, personal protection via adopting precautionary measures is one of the most effective control aspects to avoid Zika infection in the absence of suitable medical treatment. This personal protection further can be enhanced and explored by propagating information about disease prevalence. Therefore, in this study, we wish to see the effect of information on Zika transmission by formulating a compartmental mathematical model that quantifies the effect of an individual’s behavioral response as self-protection due to information. Furthermore, the basic reproduction number was calculated using the next-generation matrix technique. The model analysis was carried out to determine the local and global stability properties of equilibrium points. In addition, the model shows the occurrence of forward bifurcation when the reproduction number crosses unity. To understand the impact of various model parameters, we conducted a sensitivity analysis using both the normalized sensitivity index and the partial rank correlation coefficient methods. Moreover, we performed numerical simulations to assess the influence of important parameters on the model’s behavior for Zika prevalence. Our study accentuates that as information-induced self-protection increases, the prevalence of Zika infection will be at a very minimum level, and this observation is in line with WHO suggestions.

Abstract We observed the existence of periodic orbits in immune network under transitive solvable Lie algebra. In this article, we focus to develop condition of maximal Lie algebra for immune network model and use that condition to construct a vector field of symmetry to study nonlinear pathogen model. We used two methods to obtain analytical structure of solution, namely normal generator and differential invariant function. Numerical simulation of analytical structure exhibits correlated periodic pattern growth under spatiotemporal symmetry, which is similar to the linear dynamical simulation result. We used Lie algebraic method to understand correlation between growth pattern and symmetry of dynamical system. We employ idea of using one parameter point group of transformation of variables under which linear manifold is retained. In procedure, we present the method of deriving Lie point symmetries, the calculation of the first integral and the invariant solution for the ordinary differential equation (ODE). We show the connection between symmetries and differential invariant solutions of the ODE. The analytical structure of the solution exhibits periodic behavior around attractor in local domain, same behavior obtained through dynamical analysis.

Abstract In this study, we present a variational multiscale stabilized finite element method for steady-state incompressible fluid flow under magnetic forces. In particular, an algebraic approach of approximating the subscales has been considered, and then, the stabilization parameters are derived using Fourier analysis. The proposed scheme is used to trace the blood flow dynamics in complex arterial vessels under multiple pathological conditions. We examine the pressure and stress distribution in addition to the flow pattern to assess the criticality of the diseased condition.

Abstract This work builds machine learning models for the dataset generated using a numerical model developed on an idealized human artery. The model has been constructed accounting for varying blood characteristics as it flows through arteries with variable vascular properties, and it is applied to simulate blood flow in the femoral and its continued artery. For this purpose, we designed a pipeline model consisting of three components to include the major segments of the femoral artery: CFA, the common femoral artery and SFA, the superficial artery, and its continued one, the popliteal artery (PA). A notable point of this study is that the features and target variables of the former component pipe form the set of features of the latter, thus resulting in multicollinearity among the features in the third component pipe. Thus, we worked on understanding the effect of these correlated features on the target variables using regularized linear regression models, ensemble, and boosting algorithms. This study highlighted the blood velocity in CFA as the primary influential factor for wall shear stress in both CFA and SFA. Additionally, it established the blood rheology in PA as a significant factor for the same in it. Nevertheless, because the study relies on idealized conditions, these discoveries necessitate thorough clinical validation.

Abstract In this research, we have introduced compartments for asymptomatic and symptomatic individuals, along with reduced susceptibility, as key factors defining our investigation. The study is carried out in diverse scenarios, considering them as crucial for the essential generation number of the model, set at 3.18( r 0 > 1 {r}_{0}\gt 1 ). The persistent reproduction differential method was used to explore the impact of continuous adrenocorticotropic hormone (ACTH) administration on the global gene expression in primary cultures of both fetal and adult adrenal cells. The study also investigates ACTH’s genetic effects on both adult and fetal human adrenal cells. The conclusion of this study is demonstrated through relevant and correct medical applications.

Abstract In this article, we present a susceptible, exposed, infected, hospitalized and recovered compartmental model for COVID-19 with vaccination strategies and mask efficiency. Initially, we established the positivity and boundedness of the solutions to ensure realistic predictions. To assess the epidemiological relevance of the system, an examination is conducted to ascertain the local stability of the endemic equilibrium and the global stability across two equilibrium points are carried out. The global stability of the system is demonstrated using Lyapunov’s direct method. The disease-free equilibrium is globally asymptotically stable when the basic reproduction number (BRN) is less than one, whereas the endemic equilibrium is globally asymptotically stable when BRN is greater than one. A sensitivity analysis is performed to identify the influential factors in the BRN. The impact of various time-dependent strategies for managing and regulating the dynamic transmission of COVID-19 is investigated. In this study, Pontryagin’s maximum principle for optimal control analysis is used to identify the most effective strategy for controlling the disease, including single, coupled, and threefold interventions. Single-control interventions reveal physical distancing as the most effective strategy, coupled measures reduce exposed populations, and implementing all controls reduces susceptibility and infections.