Компьютерные исследования и моделирование

Banana Bunch Top Disease (BBTD) is a severe viral infection that poses a significant threat to banana production in tropical regions. Caused by the Banana Bunchy Top Virus (BBTV) and transmitted primarily by the banana aphid (Pentalonia nigronervosa), BBTD results in stunted growth and poor fruit production, leading to substantial economic losses. This paper presents a mathematical model to analyze the transmission dynamics of BBTD in banana plants and evaluate various control strategies using the Next Generation Matrix approach to compute the basic reproduction number R0. The study reveals that effective control of aphid populations, timely removal of infected plants, and the use of virus-free planting material significantly reduce the spread of BBTV and improve plant health. Increasing the removal rate γ and managing the transmission rate β are crucial strategies for controlling the disease, while elevated aphid infection rates λ and progression rates σ exacerbate its spread. Numerical simulations highlight the effectiveness of targeted interventions, including the application of pesticides and the introduction of resistant banana varieties. The study recommends that, in addition to current control measures, more focus should be placed on comprehensive monitoring programs, early detection of symptoms, and community education on BBTD management strategies. Enhanced efforts in these areas are crucial to reducing the incidence of BBTD and improving the resilience of banana crops.

Dengue virus transmitted by mosquitoes, poses a significant global health threat, affecting millions of people annually. In this paper, we explore the dynamics of a dengue virus transmission model, structured as an epidemiological mathematical framework. The model divides the total population into seven compartments: susceptible humans S(t), exposed humans E(t), infected humans I(t), recovered humans R(t), susceptible mosquitoes M(t), exposed mosquitoes ME(t), and infected mosquitoes MI(t). We employed the Chebyshev polynomial-exponential method (CPEM) and Tamimi-Ansari method (TAM) to conduct an in-depth semi-analytical examination of this model. The numerical simulation using MATLAB® ode45 solver was used to compare the results with CPEM and TAM, validating the accuracy and effectiveness of the obtained solutions. The comparison shows no significant differences between the CPEM with numerical results, which leads to a interesting findings. Additionally, by varying the sensitive parameters, we analyzed the behavior of the different compartments within the model. This investigation provides valuable insights into the responses of dengue transmission under various conditions, demonstrating the potential of novel semi-analytical methods for studying epidemiological models of infectious diseases, which is highly beneficial for researchers in the field.