Mathematical analysis and prediction of future outbreak of dengue on time-varying contact rate using machine learning approach.

This article introduces a novel mathematical model analyzing the dynamics of Dengue in the recent past, specifically focusing on the 2023 outbreak of this disease. The model explores the patterns and behaviors of dengue fever in Bangladesh. Incorporating a sinusoidal function reveals significant mid-May to Late October outbreak predictions, aligning with the government's exposed data in our simulation. For different amplitudes (A) within a sequence of values (A = 0.1 to 0.5), the highest number of infected mosquitoes occurs in July. However, simulations project that when ßM = 0.5 and A = 0.1, the peak of human infections occurs in late September. Not only the next-generation matrix approach along with the stability of disease-free and endemic equilibrium points are observed, but also a cutting-edge Machine learning (ML) approach such as the Prophet model is explored for forecasting future Dengue outbreaks in Bangladesh. Remarkably, we have fitted our solution curve of infection with the reported data by the government of Bangladesh. We can predict the outcome of 2024 based on the ML Prophet model situation of Dengue will be detrimental and proliferate 25 % compared to 2023. Finally, the study marks a significant milestone in understanding and managing Dengue outbreaks in Bangladesh.

Prediction and mathematical analysis of the outbreak of coronavirus (COVID-19) in Bangladesh.

In this study based on Bangladesh, a modified SIR model is produced and analysed for COVID-19. We have theoretically investigated the model along with numerical simulations. The reproduction number (R0) has been calculated by using the method of the next-generation matrix. Due to the basic reproduction number, we have analysed the local stability of the model for disease-free and endemic equilibria. We have investigated the sensitivity of the reproduction number to parameters and calculate the sensitivity indices to determine the dominance of the parameters. Furthermore, we simulate the system in MATLAB by using the fourth-order Runge-Kutta (RK4) method and validate the results using fourth order polynomial regression (John Hopkins Hospital (JHH), 2020). Finally, the numerical simulation depicts the clear picture of the upward, and the downward trend of the spread of this disease along with time in a particular place, and the parameters in the mathematical model indicate this change of intensity. This result represents, the effect of COVID-19 from Bangladesh's perspective.

Chaotic dynamics and diffusion in a piecewise linear equation.

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.