Transmission Dynamics and Optimal Control Strategies of a Hand-Foot-Mouth Disease Model with Treatment and Vaccination Interventions

In this article, the transmission dynamics of a Hand-Foot-Mouth disease model with treatment and vaccination interventions are studied. We calculated the basic reproduction number and proved the global stability of disease-free equilibrium when R0 R0 > 1. Meanwhile, we obtained the optimal control strategies minimizing the cost of intervention and minimizing the infected person. We also give some numerical simulations to verify our theoretical results.

Threshold Dynamics of a Vector-Borne Epidemic Model for Huanglongbing with Impulsive Control

In this paper, the basic reproduction number is calculated for Huanglongbing (HLB) model with impulses which is a vector-borne epidemic model with impulses. For controlling HLB, farmers’ experience is replanting of healthy plants and removing infected plants. To reflect the real world, we construct an impulsive control model which considers replanting of healthy plants and removing infected plants at one fixed time. By analyzing the model, we conclude that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number Ro 1, and we prove that the HLB is permanence if the basic reproduction number Ro > 1.

Global Dynamic Analysis of a Vector-Borne Plant Disease Model with Discontinuous Treatment

This paper proposes a vector-borne plant disease model with discontinuous treatment strategies. Constructing Lyapunov function and applying non-smooth theory to analyze discontinuous differential equations, the basic reproductive number R0 is proved, which determines whether the plant disease will be extinct or not. If R0 R0 > 1 , there exists a unique endemic equilibrium which is globally stable. The numerical simulations are provided to verify our theoretical results, which indicate that after infective individuals reach some level, strengthening treatment measures is proved to be beneficial in controlling disease transmission.

The Stochastic Coupling of SLE on the Strip Domain

The main work of this paper is to discuss the stochastic coupling of stirp SLEk (k ∈ (0,4]) on the stirp region Sπ. By constructing a bounded continuous local martingale, we prove that when a certain ordinary differential equation is satisfied, there is a coupling of two strip SLEk traces in Sπ;one is from a to b;the other is from b to a, such that the two curves visit the same set of points.

Dynamic of Non-Autonomous Vector Infectious Disease Model with Cross Infection

In the article, we established a non-autonomous vector infectious disease model, studied the long-term dynamic behavior of the system, and obtained sufficient conditions for the extinction and persistence of infectious diseases by constructing integral functions.

Pulse Roguing Strategy in a Pine Wilt Disease Epidemic Model with General Nonlinear Incidence Rate

In this study, we investigate a pine wilt transmission model with general nonlinear incidence rates and time-varying pulse roguing. Using the stroboscopic map and comparison theorem, we proved that the disease-free equilibrium is global attractive determined by the basic reproduction number R1 < 1, and in such a case, the endemic equilibrium does not exist. The disease uniformly persists only if R2 > 1.