Mathematical Analysis of the Concomitance of Illicit Drug Use and Banditry in a Population

One of the majors global health and social problem facing the world today is the use of illicit drug and the act banditry. The two problems have resulted into lost of precious lives, properties and even a devastating effects on the economy of some countries where such acts were been practiced. Of interest in this work is to study the global stability of illicit drug use spread dynamics with banditry compartment using a dynamical system theory approach. Illicit drug use and banditry reproduction number was evaluated analytically, which measures the potential spread of the illicit drug use and banditry in the population. The system exhibits supercritical bifurcation property, telling us that local stability of an illicit drug and banditry-present equilibrium exist and it is unique. In addition, the illicit drug and banditry-free and illicit drug and banditry-present equilibria were shown to be global asymptotically stable, this was achieved by construction of suitable Lyapunov functions. Sensitivity analysis was carried out to know the impact of each parameter on the dynamical spread of illicit drug use and banditry in a population. Numerical simulations were used to validate the obtained quantitative results, and examine the effects of some key parameters on the system. It was discovered that, to reduce the burden of banditry in the population, stringent control measures must be put in place to reduce the use of illicit drug in a population. Suggested control measures to use in curtail the menace of the illicit drug use and banditry were recommends.

Tracking COVID-19 Decease Through Rolling Conditional Variance

The effects of COVID-19 have been devastating globally. However, countries have essential asymmetries regarding the disease spread dynamics and the respective mortality rates. In addition to containment strategies and boosting growth and economic development in the face of the COVID-19 pandemic, society calls for solutions that allow the development of vaccines, treatments for the disease, and especially, indicators or early warnings that anticipate the evolution of new infections and deaths. This research aims to track the total deaths caused by COVID-19 in the most affected countries by the pandemics after the approval, distribution, and implementation of vaccines from 2021. We proposed an Autoregressive Integrated Moving Average (ARIMA) specification as a first adjustment. Subsequently, we estimate the conditional variance of total deaths from an Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH). Finally, we compute a rolling density backtesting within a 7-day rolling window to demonstrate the robustness estimation for COVID-19 mortality. The work's main contribution lies in exhibiting a tracking indicator for volatility and COVID-19 direction, including a weekly window to observe its evolution.

Local Interactions Affect Spread of Resource in a Consumer-resource System With Group Defense

Integrodifference equations are a discrete time spatially explicit model that describes dispersal of ecological populations through space. This framework is useful to study spread dynamics of organisms and how ecological interactions can affect their spread. When studying interactions such as consumption, dispersal rates might vary with life cycle stage, such as cases with dispersive juveniles and sessile adults. In the non-dispersive stage, resources may engage in group defense to protect themselves from consumption. These local nondispersive interactions may limit the number of dispersing recruits that are produced and therefore affect how fast populations can spread. We present a spatial consumer-resource system using an integrodifference framework with limited movement of their adult stages and group defense mechanisms in the resource population. We model group defense using a Type IV Holling functional response, which limits survival of adult resource population and enhances juvenile consumers production. We find that high mortality levels for sessile adults can destabilize resource at carrying capacity. Furthermore, we find that at high resource densities, group defense leads to a slower local growth of resource in newly invaded regions due to intraspecific competition outweighing the effect of consumption on resource growth.

A FRACTAL-FRACTIONAL 2019-NCOV MODEL OF MAJOR DISASTER FOR HUMAN LIFE

The purpose of this research is to explore the spread dynamics of a novel coronavirus outbreak, or 2019-nCOV via a fractional approach of type fractal-fractional (FF) derivative. We considered the FF approach in sense of the Atangana–Baleanu derivative for the system 2019-nCOV. In the FF operator, when we choose fractional-order one, we achieve the fractal model and when choosing fractal order one then we obtain a fractional model and while considering both the operators together we obtain the fractal-fractional model. The obtained results show via graphics for the different collections of fractal and fractional orders. The graphical results show the new operator impacts on a practical situation in a more visual way.

Modeling the transmission dynamics of racism propagation with community resilience

Racism spreading can have a vital influence on people’s lives, declining adherence, pretending political views, and recruiters’ socio-economical crisis. Besides, Web 2.0 technologies have democratized the creation and propagation of racist information, which facilitated the rapid spreading of racist messages. In this research work, the impact of community resilience on the spread dynamics of racism was assessed. To investigate the effect of resilience-building, new SERDC mathematical model was formulated and analyzed. The racism spread is under control where $$R_0<1$$ R 0 < 1 , whereas persist in the community whenever $$R_0>1$$ R 0 > 1 . Sensitivity analysis of the parameters value of the model are conducted. The rising of transmission and racial extremeness rate provides the prevalence of racism spread. Effective community resilience decline the damages, mitigate, and eradicate racism propagation. Theoretical analysis of the model are backed up by numerical results. Despite the evidence of numerical simulations, reducing the transmission and racial extremeness rate by improving social bonds and solidarity through community resilience could control the spread of racism.

A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility

This paper investigates the impact of human activity and mobility (HAM) in the spreading dynamics of an epidemic. Specifically, it explores the interconnections between HAM and its effect on the early spread of the COVID-19 virus. During the early stages of the pandemic, effective reproduction numbers exhibited a high correlation with human mobility patterns, leading to a hypothesis that the HAM system can be studied as a coupled system with disease spread dynamics. This study applies the generalized Koopman framework with control inputs to determine the nonlinear disease spread dynamics and the input-output characteristics as a locally linear controlled dynamical system. The approach solely relies on the snapshots of spatiotemporal data and does not require any knowledge of the system’s physical laws. We exploit the Koopman operator framework by utilizing the Hankel Dynamic Mode Decomposition with Control (HDMDc) algorithm to obtain a linear disease spread model incorporating human mobility as a control input. The study demonstrated that the proposed methodology could capture the impact of local mobility on the early dynamics of the ongoing global pandemic. The obtained locally linear model can accurately forecast the number of new infections for various prediction windows ranging from two to four weeks. The study corroborates a leader-follower relationship between mobility and disease spread dynam-

Simulating and visualizing infection spread dynamics with temporal networks

Temporal networks comprehend a widely adopted structure to model interactions involving a domain's instances over time. In the context of infection spread, it could be used to model face-to-face contacts among susceptible and infected individuals. By considering network visualization strategies, one can easily identify who infected whom and when, the epidemics outbreak, and other relevant behaviors. As a consequence, decision making related to the spread speed and magnitude becomes faster and more reliable. This paper presents a visual analytics approach for the simulation and analysis of infection spread dynamics that considers different infection probabilities and different levels of social distancing. We performed our experiments using two real-world social networks that represent school environments and our findings support the need for a high social distancing compliance allied to the adoption of protective measures such as the use of face masks.