Existence and stability of pseudo almost periodic solutions for shunting inhibitory cellular neural networks with neutral type delays and time-varying leakage delays.

In this paper, shunting inhibitory cellular neural networks(SICNNs) with neutral type delays and time-varying leakage delays are investigated. By applying Lyapunov functional method and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of pseudo almost periodic solutions of the model. An example is given to support the theoretical findings. Our results improve and generalize those of the previous studies.

The impact of predators of mosquito larvae on Wolbachia spreading dynamics.

Dengue fever creates more than 390 million cases worldwide yearly. The most effective way to deal with this mosquito-borne disease is to control the vectors. In this work we consider two weapons, the endosymbiotic bacteria Wolbachia and predators of mosquito larvae, for combating the disease. As Wolbachia-infected mosquitoes are less able to transmit dengue virus, releasing infected mosquitoes to invade wild mosquito populations helps to reduce dengue transmission. Besides this measure, the introduction of predators of mosquito larvae can control mosquito population. To evaluate the impact of the predators on Wolbachia spreading dynamics, we develop a stage-structured five-dimensional model, which links the predator-prey dynamics with the Wolbachia spreading. By comparatively analysing the dynamics of the models without and with predators, we observe that the introduction of the predators augments the number of coexistence equilibria and impedes Wolbachia spreading. Some numerical simulations are presented to support and expand our theoretical results.

Recurrent epidemic waves in a delayed epidemic model with quarantine.

In this paper, we are concerned with an epidemic model with quarantine and distributed time delay. We define the basic reproduction number R0 and show that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, whereas if R0>1, then it is unstable and there exists a unique endemic equilibrium. We obtain sufficient conditions for a Hopf bifurcation that induces a nontrivial periodic solution which represents recurrent epidemic waves. By numerical simulations, we illustrate stability and instability parameter regions. Our results suggest that the quarantine and time delay play important roles in the occurrence of recurrent epidemic waves.

Modeling transmission dynamics of rabies in Nepal.

Even though vaccines against rabies are available, rabies still remains a burden killing a significant number of humans as well as domestic and wild animals in many parts of the world, including Nepal. In this study, we develop a mathematical model to describe transmission dynamics of rabies in Nepal. In particular, an indirect interspecies transmission from jackals to humans through dogs, which is relevant to the context of Nepal, is one of the novel features of our model. Our model utilizes annual dog-bite data collected from Nepal for a decade long period, allowing us to reasonably estimate parameters related to rabies transmission in Nepal. Using our model, we calculated the basic reproduction number ( R 0 = 1.16 ) as well as intraspecies basic reproduction numbers of dogs ( R 0 D = 1.14 ) and jackals ( R 0 J = 0.07 ) for Nepal, and identified that the dog-related parameters are primary contributors to R 0 . Our results show that, along with dogs, jackals may also play an important role, albeit lesser extent, in the persistence of rabies in Nepal. Our model also suggests that control strategies may help reduce the prevalence significantly but the jackal vaccination may not be as effective as dog-related preventive strategies. To get deeper insight into the role of intraspecies and interspecies transmission between dog and jackal populations in the persistence of rabies, we also extended our model analysis into a wider parameter range. Interestingly, for some feasible parameters, even though rabies is theoretically controlled in each dog and jackal populations ( R 0 D < 1 , R 0 J < 1 ) if isolated, the rabies epidemic may still occur ( R 0 > 1 ) due to interspecies transmission. These results may be useful to design effective prevention and control strategies for mitigating rabies burden in Nepal and other parts of the world.

Global convergence dynamics of almost periodic delay Nicholson's blowflies systems.

We take into account nonlinear density-dependent mortality term and patch structure to deal with the global convergence dynamics of almost periodic delay Nicholson's blowflies system in this paper. To begin with, we prove that the solutions of the addressed system exist globally and are bounded above. What's more, by the methods of Lyapunov function and analytical techniques, we establish new criteria to check the existence and global attractivity of the positive asymptotically almost periodic solution. In the end, we arrange an example to illustrate the effectiveness and feasibility of the obtained results.

Impulsive releases of sterile mosquitoes and interactive dynamics with time delay.

To investigate the impact of periodic and impulsive releases of sterile mosquitoes on the interactive dynamics between wild and sterile mosquitoes, we adapt the new idea where only those sexually active sterile mosquitoes are included in the modelling process and formulate new models with time delay. We consider different release strategies and compare their model dynamics. Under certain conditions, we derive corresponding model formulations and prove the existence of periodic solutions for some of those models. We provide numerical examples to demonstrate the dynamical complexity of the models and propose further studies.

Global asymptotical stability of almost periodic solutions for a non-autonomous competing model with time-varying delays and feedback controls.

In this paper, we are concerned with a non-autonomous competing model with time delays and feedback controls. Applying the comparison theorem of differential equations and by constructing a suitable Lyapunov functional, some sufficient conditions which guarantee the existence of a unique globally asymptotically stable nonnegative almost periodic solution of the system are established. An example with its numerical simulations is given to illustrate the feasibility of our results.

Modeling transmission dynamics of lyme disease: Multiple vectors, seasonality, and vector mobility.

Lyme disease is the most prevalent tick-borne disease in the United States, which humans acquire from an infected tick of the genus Ixodes (primarily Ixodes scapularis). While previous studies have provided useful insights into various aspects of Lyme disease, the tick's host preference in the presence of multiple hosts has not been considered in the existing models. In this study, we develop a transmission dynamics model that includes the interactions between the primary vectors involved: blacklegged ticks (I. scapularis), white-footed mice (Peromyscus leucopus), and white-tailed deer (Odocoileus virginianus). Our model shows that the presence of multiple vectors may have a significant impact on the dynamics and spread of Lyme disease. Based on our model, we also calculate the basic reproduction number, R 0 , a threshold value that predicts whether a disease exists or dies out. Subsequent extensions of the model consider seasonality of the tick's feeding period and mobility of deer between counties. Our results suggest that a longer tick peak feeding period results in a higher infection prevalence. Moreover, while the deer mobility may not be a primary factor for short-term emergence of Lyme disease epidemics, in the long-run it can significantly contribute to local infectiousness in neighboring counties, which eventually reach the endemic steady state.

Global exponential stability of positive periodic solution of the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays.

In this paper, we study the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.