Communication in Biomathematical Sciences

Effects of Nonlocal Seed Dispersal on Vegetation Dynamics in Arid Environments

Riya Akter, Muhammad Humayun Kabir

This article investigates the effects of nonlocal seed dispersal on vegetation dynamics
in arid environments by developing and analyzing a mathematical model. The model is
formulated as a system of coupled nonlinear partial differential equations that describe the
interaction between water and plant biomass, incorporating both local diffusion of water
and nonlocal dispersal of plants. The nonlocal dispersal is equipped with a suitable kernel
function, which captures the spatially extended movement of seeds. To simplify the analysis,
we focus on the spatially homogeneous version of the model, which yields a system of
nonlinear ordinary differential equations. We establish the well-posedness of the system by
proving the existence, uniqueness, nonnegativity, and boundedness of solutions. We determine
the steady states and analyze their local stability, using phase portraits to illustrate
the qualitative behavior of the system. Bifurcation and sensitivity analyses are performed to
understand how key parameters such as rainfall rate, plant mortality, and dispersal parameter
control the system’s dynamics and transitions. Numerical simulations using the classical
Runge–Kutta 4th–order method further validate the analytical results and reveal the effect
of the dispersal control parameter b. These findings highlight the ecological relevance of
nonlocal dispersal and provide insights into vegetation dynamics in dryland systems, even
in the absence of explicit spatial structure.

Glucose–Insulin System- Fuzzy Delay modelling under cross product

SWAPNILA NIGAM

Glucose–insulin regulation is central to metabolic control and the mathematical study of diabetes dynamics. This paper investigates a fuzzy delay differential model for glucose–insulin interaction under parameter uncertainty using the Ban–Bede cross product. Existence and uniqueness of fuzzy solutions are established under suitable Lipschitz conditions, followed by equilibrium analysis and local stability criteria. Hopf bifurcation analysis identifies the critical delay inducing oscillatory behaviour. Fuzzy Euler and fourth-order Runge Kutta methods are developed for numerical approximation, with their consistency, stability, and convergence established. Numerical simulations validate the theoretical results and demonstrate the effects of delay and
uncertainty on glucose–insulin dynamics.

Hybrid Epidemiological Feature Engineering for Intelligent Random Forest-Based COVID-19 Forecasting: A Comparative Analysis of Italy and India

Bagher Javadi, Supajit Sraphet

Abstract- Accurate forecasting of infectious disease transmission is essential for effective public health planning and epidemic control. However, the highly nonlinear and dynamic behavior of Coronavirus Disease 2019 (COVID-19) presents significant challenges for conventional statistical forecasting techniques. This study proposes a hybrid epidemiological feature engineering framework based on Random Forest regression for forecasting daily COVID-19 cases in Italy and India. Daily epidemiological data were collected from publicly available COVID-19 databases and preprocessed using a 7-day moving average to reduce reporting variability. Epidemiological feature engineering was performed by incorporating lag variables, rolling statistical measures, vaccination-related indicators, temporal attributes, and the effective reproduction number (Rt) into the forecasting framework. The predictive performance of Random Forest was compared with Autoregressive Integrated Moving Average (ARIMA), Seasonal Autoregressive Integrated Moving Average (SARIMA), and a hybrid ARIMA–Random Forest model using a chronological 70:30 training–testing strategy. Forecasting accuracy was evaluated using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Symmetric Mean Absolute Percentage Error (sMAPE). The Random Forest model consistently achieved the highest forecasting accuracy for both countries, substantially outperforming the statistical and hybrid approaches. Feature importance analysis demonstrated that short-term temporal indicators, particularly rolling mean and lag-based variables, contributed most strongly to forecasting performance, whereas vaccination-related variables provided complementary predictive information. These findings demonstrate that epidemiological feature engineering combined with ensemble machine learning provides a robust framework for short-term COVID-19 forecasting and offers a practical decision-support tool for epidemic surveillance and future infectious disease preparedness.

Stability Analysis of an SEIVR Epidemic Model with Waning Immunity and Vaccination: Application to COVID-19 Dynamics in Bangladesh

Standard SEIR models with permanent immunity cannot capture the waning natural and
vaccine-induced protection that contributed to Bangladesh’s 2021 COVID-19 Delta wave. We
formulate and analyze a five-compartment SEIVR model with bidirectional waning immunity and
complete temporary vaccine protection. Using the next-generation matrix method, we derive a
closed-form basic reproduction number R0, prove local asymptotic stability of the disease-free
equilibrium for R_0 < 1, and establish a conditional global stability result whose conditions are
satisfied by neither baseline parameter set used. For R_0 > 1, we prove existence and uniqueness
of the endemic equilibrium in closed form; numerical evidence indicates local stability and a
broad basin of attraction, consistent with a forward transcritical bifurcation. A local sensitivity
analysis, corroborated by global LHS-PRCC, identifies transmission, recovery, vaccination, and
vaccine-waning rates as dominant drivers of R_0, which is analytically independent of natural
immunity waning despite it shaping the endemic burden. A literature-informed comparison with
normalized Bangladesh Delta-wave data yields a normalized RMSE of 0.19 and correlation of
0.81; the required vaccination rate is approximately 96% higher than the assumed daily rate. The
novelty combines an explicit global-stability boundary, a separation between the invasion threshold
and endemic burden, and a numerically supported bifurcation structure.