Mohd Hafiz Mohd

The health and sustainability of honeybee populations are essential for global food production and ecological balance. More than one-third of agricultural crops depend on pollination, making honeybees indispensable to the global economy. However, colonies worldwide are increasingly threatened by the gut parasite Nosema ceranae , whose recurrent outbreaks cause severe productivity losses and economic damage to the apicultural and agricultural sectors. Despite its prevalence, the nonlinear mechanisms responsible for the persistence and resurgence of Nosema ceranae remain poorly understood. This study aims to develop a mathematical model that interpret the complex epidemiological behaviour of Nosema ceranae under realistic biological conditions, specifically focusing on renewal of colony-level susceptibility and the strained resources available for control and management. A nonlinear Susceptible-Infected-Recovered-Susceptible (SIRS) model incorporating renewal of colony-level susceptibility and resource saturation is formulated and analysed using stability theory and numerical bifurcation techniques. Analytical derivations identify the conditions for transcritical and Hopf bifurcations, while numerical continuation analysis and time series simulations validate the theoretical predictions and reveal the rich dynamical structure. The analysis uncovers two critical thresholds governing colony dynamics. A forward (transcritical) bifurcation marks the transition from disease eradication to endemic persistence, while a Hopf bifurcation arising from resource limitations induces sustained oscillations representing recurrent infection waves. The coexistence of stable equilibria and periodic orbits highlights bistability, indicating that small perturbations or change in control interventions can trigger large amplitude outbreaks. These nonlinear feedbacks provide a mechanistic explanation for the cyclical prevalence of Nosema ceranae observed in distinct colonies. The proposed framework establishes, for the first time, how the interplay between partial recovery and limited resource availability can drive complex epidemic patterns in honeybee colonies. Beyond its theoretical contribution, the study provides actionable insight for the agriculture industry: efficient allocation of control resources and timely interventions are essential to prevent recurrent epidemics that threaten pollination services and agricultural productivity. The results bridge mathematical modelling and ecological management, offering a predictive foundation for mitigating the economic and environmental impact of Nosema ceranae on global food security.

This study compares the newly developed stochastic agent-based model (ABM) and deterministic system within the context of COVID-19 transmission dynamics, using the Susceptible-Exposed-Infectious-Removed-Perception (SEIRP) compartments. The primary aim is to analyse the similarities and differences between these modelling approaches, providing insights into the emergent behaviours of the epidemiological systems. We also investigate how social phenomena like public perception affect the two epidemiological models’ outcomes, focusing on scenarios with varying awareness levels and proportions of severe cases. Our results show that while deterministic model outputs align well with the ABM for large populations, discrepancies emerge for small populations in the ABM due to the impacts of stochastic extinction and discreteness of individuals. In scenarios with high proportions of severe cases and for large population sizes, the deterministic model exhibits oscillatory behaviour. In this situation, the averaged ABM densities initially capture the fluctuation dynamics when a substantial number of realisations is used in simulation; however, this stochastic system exhibits diminishing fluctuations across different realisations, contributing to a consistent average akin to an endemic steady state over a longer period. Interestingly, as the number of realisations is reduced, the agreement between stochastic and deterministic systems in depicting recurrent outbreaks is evident (i.e., realisations-dependent dynamical behaviour). In the next case study, the joint effect of recovery, latency period, disease severity and public perception is explored, highlighting how different factors can combine to influence the systems’ outcomes. Notably, our case study finds that even when the deterministic model demonstrates the persistence of sustained oscillations, the ABM can depict an extinction state; this stochastic ABM observation is caused by the realisations in this epidemiological system fluctuating to a very low population density and being excluded over a long run. Overall, our findings suggest the importance of considering both deterministic and stochastic models in infectious disease modelling, highlighting the need for comprehensive analyses to guide evidence-based decision-making in public health and epidemiology.

The first chapter of the book serves as an essential introduction to the field of mathematical modelling and its significance in engineering and the physical sciences. This chapter provides a foundation for readers by outlining the objectives, scope, and structure of the book while demonstrating the importance of mathematical modelling as a problem-solving tool. The chapter begins by highlighting the critical role of mathematical modelling in addressing complex engineering problems and understanding physical phenomena. It highlights the subsequent chapters’ focus on specific applications of mathematical modelling in engineering disciplines and the physical sciences. The importance of case studies and practical examples throughout the book is also emphasised, as they bridge the gap between theory and real-world applications.

Exothermic biocatalytic reactions are chemical reactions catalysed by enzymes that can result in the release of heat energy. These reactions are becoming increasingly important in the field of industrial chemistry due to their effectiveness, environmental friendliness, and ability to minimize waste. In this study, we consider an enzyme-catalysed reaction-diffusion system, which is modelled using partial differential equations (PDE). This PDE model is studied using numerical simulation and bifurcation analysis techniques to uncover the effect of diffusion on enzyme-substrate reaction system. Some intriguing bifurcational changes in dynamics e.g., co-dimension one bifurcations, which can give rise to distinct steady states and oscillatory solutions in this enzyme-catalysed are observed. These findings can aid in understanding the biochemical processes involving enzymes and their overall dynamics. The mathematical modelling also offers invaluable insights into the mechanisms of enzyme-catalysed reactions and diffusion effects, which are fundamental to the study of biochemical processes. Result from the dynamical analysis certainly support in silico engineering evaluations by aiming to optimise the operating conditions of a reactor, thus saving considerable experimental effort.

This study aims to review recent research on the collective behaviour of excitatory and inhibitory (E-I) spiking neural networks. The research methodology used is Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) procedures, comprising three primary stages: an initial search for literature in the SCOPUS database, a screening process based on specific inclusion and exclusion criteria, and a review of the selected literatures. Out of 491 documents from 2014 to 2024, 6 research papers are qualified for review. Four distinct dynamical states have been identified: synchrony, irregular behaviour, stationary state, and oscillatory dynamics. Our review findings suggest that the collective dynamics of E-I spiking neurons stem from the interaction of intrinsic neuronal characteristics, balance mechanisms, and the type of external stimuli. Additionally, the widespread use of Quadratic Integrate-and-Fire (QIF) neurons in the literature highlights its significance as a robust candidate for exploring collective behaviours in large-scale neuronal networks.