Dynamic analysis of a malaria reaction-diffusion model with periodic delays and vector bias

<abstract><p>One of the most important vector-borne disease in humans is malaria, caused by <italic>Plasmodium</italic> parasite. Seasonal temperature elements have a major effect on the life development of mosquitoes and the development of parasites. In this paper, we establish and analyze a reaction-diffusion model, which includes seasonality, vector-bias, temperature-dependent extrinsic incubation period (EIP) and maturation delay in mosquitoes. In order to get the model threshold dynamics, a threshold parameter, the basic reproduction number $ R_{0} $ is introduced, which is the spectral radius of the next generation operator. Quantitative analysis indicates that when $ R_{0} &lt; 1 $, there is a globally attractive disease-free $ \omega $-periodic solution; disease is uniformly persistent in humans and mosquitoes if $ R_{0} &gt; 1 $. Numerical simulations verify the results of the theoretical analysis and discuss the effects of diffusion and seasonality. We study the relationship between the parameters in the model and $ R_{0} $. More importantly, how to allocate medical resources to reduce the spread of disease is explored through numerical simulations. Last but not least, we discover that when studying malaria transmission, ignoring vector-bias or assuming that the maturity period is not affected by temperature, the risk of disease transmission will be underestimate.</p></abstract>

Global dissipativity of non-autonomous BAM neural networks with mixed time-varying delays and discontinuous activations

In this paper, we investigate the dissipativity of a class of BAM neural networks with both time-varying and distributed delays, as well as discontinuous activations. First, the concept of the Filippov solution is extended to functional differential equations with discontinuous right-hand sides via functional differential inclusions. Then, by constructing Lyapunov functional and employing a generalized Halanay inequality, several sufficient easy-to-test conditions are successfully obtained to guarantee the global dissipativity of the Filippov solution of the considered system. The derived results extend and improve some previous publications on conventional BAM neural networks. Meanwhile, the estimations of the positive invariant and globally attractive set are given. Finally, numerical simulations are provided to demonstrate the effectiveness of our proposed results.

Dynamics of Infectious Diseases: Local Versus Global Awareness

Public awareness programs may deeply influence the epidemic pattern of a contagious disease by altering people’s perception of risk and individuals behavior during the course of the epidemic outbreak. Regardless of the veracity, social media advertisements are expected to execute an increasingly prominent role in the field of infectious disease modeling. In this paper, we propose a model which portrays the interplay between dissemination of awareness at local and global levels, and prevalence of disease. Our sensitivity results determine the correlations between some epidemiologically important parameters and disease prevalence. The growth rate of broadcasting information through social media is found to destabilize the system through limit cycle oscillations whereas the baseline number of social media advertisements stabilize the system by terminating persistent oscillations. The system first undergoes supercritical Hopf-bifurcation and then subcritical Hopf-bifurcation on gradual increase in dissemination rate of awareness at local/global level. Moreover, the disease is eradicated if the dissemination rates of awareness and baseline number of social media advertisements are too large. We also study the effect of seasonal variation of the growth rate of social media advertisements. Our nonautonomous system generates globally attractive positive periodic solution if the growth rate of social media advertisements lies between certain ranges. However, the global attractivity is affected on enhancement in growth rate of social media advertisements and three-periodic solution is observed. Our findings show that baseline number of social media advertisements and dissemination of awareness at individual as well as community levels play a tremendous role in eliminating the burden of disease. Furthermore, a comparison of the effects of local and global awareness reveals that the latter is more effective in curtailing the disease. We believe these findings may be beneficial to understand the contagion characteristics of real epidemics and help to adopt suitable precautionary measures in the form of nonpharmaceutical interventions.

On the dynamics of the impulsive predator-prey systems with Beddington – DeAngelis type functional response

UDC 517.9 In this study, the two-dimensional predator-prey system with Beddington–DeAngelis type functional response with impulses is considered in a periodic environment. For this special case, necessary and sufficient conditions are found for the considered system when it has at least one -periodic solution. This result is mainly based on the continuation theorem in the coincidence degree theory and to get the globally attractive -periodic solution of the given system, an inequality is given as the necessary and sufficient condition by using the analytic structure of the system.

Physical activity, sport and transnational migrant spaces in Shanghai, China: (Re)crafting contours of a metropolitan cityscape

This study examines associations between sport/physical activity space, community formation and social life among Shanghai’s highly skilled migrant demographic. There is limited illustration of the roles sport and physical exercise provision and spaces play in this migrant cohort’s lives, community formation and participation in their host societies. Yet, such evidence is of value in determining social policy, urban development and community engagement initiatives. Using a mixed-methods approach involving public policy critique, cultural and spatial analysis and virtual community investigation, this article provides a conceptual exploration of ways sport and physical activity frame individual and collective migrant experiences, and how such experiences enmesh with wider geo-spatial, political and domestic context. Amid Shanghai’s presentation as a globally attractive space, we reveal some of the complexities of the cityscape as an emblematic location for highly mobile, highly skilled migrants. A confluence of ideals about urban citizenship, social participation and localised physical activity/sport-based (inter)action, we note, articulate Shanghai anew, and contribute to debates on highly skilled transnational mobility and community formation.

On the Throughput Optimization in Large-Scale Batch-Processing Systems

We analyze a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function that arises due to overhead amortization. In practice, throughput optimization relies on numerical searches for the optimal batch size which is computationally cumbersome. In this paper, we model this system in terms of a closed queueing network assuming certain forms of service speedup; a standard Markovian analysis yields the optimal throughput in w n4 time. Our main contribution is a mean-field model that has a unique, globally attractive stationary point, derivable in closed form. This point characterizes the asymptotic throughput as a function of the batch size that can be calculated in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

Global dynamics of a stage-structured hantavirus infection model with seasonality

In this paper, we study a time-periodic model, which incorporates seasonality and host stage-structure. This model describes the propagation of Puumala hantavirus within the bank vole population of Clethrionomys glareolus. The basic reproduction number R0 is obtained. By appealing to the theory of monotone dynamical systems and chain transitive sets, we establish a threshold-type result on the global dynamics in terms of R0, that is, the virus-free periodic solution is globally attractive, and the virus dies out if R0 ≤ 1, while there exists a unique positive periodic solution, which is globally attractive, and the virus persists if R0 > 1. Numerical simulations are given to confirm our theoretical results and to show that cleaning environment and controlling the grow of mice population are essential control strategies to reduce hantavirus infection.

A new approach to persistence and periodicity of logistic systems with jumps

<abstract><p>This paper considers a class of logistic type differential system with jumps. Based on discontinuous control theory, a new approach is developed to guarantee the persistence and existence of a unique globally attractive positive periodic solution. The development results of this paper emphasize the effects of jumps on system, which are different from the existing ones in the literature. Two examples and their simulations are given to illustrate the effectiveness of the proposed results.</p></abstract>