The interplay between criminal activity and crime control/prevention measures is inherently dynamic. This paper presents a simple nonlinear dynamical system in which criminal activity levels are coupled to policing effort. Through the process of non-dimensionalisation and sensitivity analysis, policing efficiency and the responsiveness of policing effort are identified as key parameter groupings. An analysis of the system shows that bi-stability is a feature of the dynamics. When there is no feedback between criminal activity and police recruitment, a saddle-node bifurcation occurs and threshold levels of criminal activity are required for the activity to be maintained. When feedback is permitted, we also find a backward bifurcation and criminal activity can be contained for policing efficiency below its threshold level. We demonstrate proof of concept for how the model might be used as a predictive tool with real data.

This study investigates the dynamics of cochlear hair cell populations under environmental stressors such as prolonged exposure to loud noise from earphones. To understand potential temporary hearing loss dynamics due to earphones, a mathematical model is developed in this investigation to capture the behavior of healthy, fatigued, and impaired hair cells in response to varying sound intensities, described by differential equations incorporating sound intensity and its regulation. The model is scaled and analysis of the system's steady states show that two endemic equilibria exist, with local asymptotic stability investigated using the Jacobian matrix. Results show that there is a critical level of sound exposure above which the auditory system can no longer maintain a healthy state, leading to long-term hearing impairment. Simulation results show that for a given intensity level, hearing loss is inevitable for certain for specific Temporary Threshold Shift (TTS). We are able to quantify healthy and acceptable TTS levels, beyond which there are no healthy, fatigued or impaired hair cells. The results can be used to predict hearing impairment outcomes and guide evidence-based interventions to mitigate the adverse effects of prolonged low-pressure sound exposure on auditory health.

This study extends the post-Keynesian framework for cyclical economic growth, initially proposed by Goodwin in 1967, by integrating government intervention to stabilize employment amidst wage mismatches. Given the pressing challenges of unemployment and wage disparity in developing economies, particularly South Africa, this extension is necessary to better understand how policy interventions can influence labor market dynamics. Central to the study is the endogenous interaction between capital and labor, where class dynamics influence economic growth patterns. The research focuses on the competitive relationship between real wage growth and its effects on employment. Methodologically, the study measures the impact of intervention strategies using a system of coupled ordinary differential equations (Lotka–Volterra type), along with econometric techniques such as quantile regression, moving averages, and mean absolute error to measure wages mismatch. Results demonstrate the inherent contradictions of capitalism under intervention, confirming established theoretical perspectives. This work further contributes to economic optimality discussions, especially regarding the timing and persistence of economic cycles. The model provides a quantifiable approach for formulating intervention strategies to achieve long-term economic equilibrium and sustainable labor–capital coexistence.

The COVID-19 pandemic critically exposed public health vulnerabilities and the intricate challenges of international policy coordination. While extensive research has independently explored infection rates and governmental responses, a significant gap persists in understanding how structural similarities in pandemic dynamics relate to regional, geographic, or economic interdependence. Addressing this crucial gap, this study employs Topological Data Analysis (TDA), specifically the Mapper algorithm, to analyze normalized COVID-19 case data up to the end of 2022, segmented into epidemiological waves, across 15 European countries. We integrate this analysis with both average and wave-specific policy stringency scores and established group membership data (for example, Eurozone, Schengen Area, Visegrád Group) to identify clusters of nations exhibiting analogous wave profiles. Furthermore, geographic neighbor relationships are incorporated to examine the intersection of spatial and dynamic proximity. Our findings demonstrate that topological similarity in pandemic trajectories does not consistently correlate with formal economic or geographic affiliations, and countries can appear in multiple clusters, revealing transitional epidemic profiles. Statistical analyses reveal no significant variation in policy stringency among these clusters, suggesting that shared economic frameworks did not inherently drive coordinated pandemic responses. Robustness checks using alternative wave segmentations and daily stringency data confirm the stability of these results. These results are critical for understanding the complex, multi-faceted nature of national pandemic responses and provide a novel framework for assessing the effectiveness and alignment of public health strategies beyond traditional geopolitical boundaries.