Communication in Biomathematical Sciences

Predator Persistence Threshold and Transcritical Bifurcation in a Predator-Prey Model with Dynamic Alternative Food

Resmawan Resmawan, Novianita Achmad, Maya Rayungsari, Binti Mualifatul Rosydah

This study develops a predator–prey model by considering alternative food as a dynamic variable. Unlike previous models that treat alternative food as a constant parameter, the proposed model assumes that alternative food can regenerate logistically and be consumed by the predator. The model incorporates logistic prey growth, prey group defense, a predation response influenced by alternative food, predator ecological costs, and the growth dynamics of alternative food. The analysis includes fundamental properties of the model, equilibrium existence, local stability, predator persistence threshold, sensitivity analysis of the critical threshold, transcritical bifurcation analysis, and numerical simulations. The analytical results show that the model admits several biologically feasible equilibrium points, including the predator-free equilibrium and the interior equilibrium representing the coexistence of prey, predator, and alternative food. The predator-free equilibrium is governed by the predator invasion eigenvalue, which leads to a critical threshold $L_c$ for the carrying capacity of alternative food. When $L < L_c$ , the predator-free equilibrium is stable and the predator cannot persist. Conversely, when $L > L_c$ , the predator-free equilibrium loses stability and a stable interior equilibrium branch emerges, indicating a transcritical bifurcation. Sensitivity analysis shows that the threshold $L_c$ is strongly influenced by predator conversion efficiency, predator mortality, prey group defense, predation saturation, and predator efficiency in utilizing alternative food. Numerical simulations confirm the analytical results through three-dimensional phase portraits, time series, one-parameter bifurcation diagrams, and a two-parameter threshold region in the $(L,θ)(L,\theta)$ plane. Biologically, the results emphasize that alternative food availability alone is not sufficient to maintain predator persistence; its regeneration capacity must be adequate and the associated ecological cost must remain sufficiently low.

Mathematical Modeling of PGPR Growth Using General Complex Integral Transform on Time Scales.

Dipali Kaklij, Dinkar Patil, Padmini Wagh

Cow urine and jaggery (CJ media) were used in place of synthetic Nutrient Broth to create an alternate, more affordable medium for PGPR bacterial growth. In order to test four formulations (CJ-A, CJ-B, CJC, and CJ-D), 24-hour-old cultures were inoculated, and growth was measured at 600 nm using a UV-visible spectrophotometer. Among these, CJ-D outperformed the conventional nutritional broth and other CJ formulations in terms of bacterial growth. Cost analysis showed a considerable decrease, with CJ media costing Rs. 2.32/L as opposed to Rs. 99.15/L for nutritional broth, indicating its potential for cost-effective large-scale PGPR production. The bacterial growth follows first order linear dynamic equation on time scales. We derive the exact solution of the proposed model and analyse the behaviour on the time scales by using General Complex Integral Transform on Time Scales. The model validates experimental observations.

Ideal Retinal Disease Classification using Deep Learning Techniques

MANORANJAN DASH

Vision and eye health are two of the most crucial components of human life that must be safeguarded in order for individuals to survive. Retinal injury is the most frequent cause of eye conditions such Choroidal Neovascularization (CNV), DRUSEN, and Diabetic Macular Edema (DME). There is absolutely no chance of reversing or treating eyesight because the retina is injured and discovered afterwards. The patient might experience partial or complete eyesight loss as a result. The goal of this study is to create a deep learning and transfer learning classification model that, when applied to retinal scans obtained from an optical coherence tomography (OCT) instrument, can automatically classify various retinal illnesses. We combined the categorical cross entropy loss function with five pre-trained networks, including Xception, InceptionV3, ResNet50, VGG16, and VGG19, to produce a multi-class classification network. 84495 greyscale photos divided into four categories were used as training and testing data for the suggested approach (CNV, DME, DRUSEN and Normal). With a classification accuracy of 96.43% during the experimental evaluation, the Xception model surpassed other pre-trained networks.

Optimal Control Analysis of Age and Gender-Structured Malaria Transmission Dynamics in Nigeria

Malaria continues to be a chronic national health epidemic in Nigeria 
and despite all control measures, the spread of malaria continue, 
disproportionately impacting humans and claiming a significant share 
of the global morbidity and mortality with expectant mothers and children 
below the age of 5 been the most vulnerable, as well as adult men being 
disproportionately affected. This work extend, analyzed and evaluated 
age and gender-based mathematical model on the dynamics of malaria transmission. 
The model built upon previous age- and gender-structured models by incorporating 
optimal control measures based on each human class to curtail the spread of the disease. 
The six measures of control that were incorporated in the model include insecticide-treated 
nets, intermittent preventive treatment during pregnancy, childhood immunization, protective 
clothing to adult men, indoor residual spraying and environmental sanitation. 
Its methodology involved analytical strategy, including calculation of the effective 
reproduction number $\mathcal{R}_e$ by the method of next-generation matrix, analysis 
of the stability of Malaria-free state and optimal control analysis using the maximum 
principle of Pontryagin with numerical simulations being run in Python. 
The Model analysis yielded \(\mathcal{R}_e = 1.5374\) without controls, 
confirming endemic transmission in the modeled population while the optimal 
control simulations showed that a combination of all six control measures would 
produce the maximum reduction in infections in all compartments, with individual 
measures being considerably less effective.