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.

International Comparative Study on Education Laws of the Persons with Disabilities: An Observation on Regulations on the Education of Persons with Disabilities

The issue of education for people with disabilities has become of increasing concern. How can we effectively guarantee the basic right to education for persons with disabilities? Will the revised Regulation on Education for Persons with Disabilities meet their needs? This article takes the Regulation on Education for Persons with Disabilities as the core and compares it with the related special educational laws of the United States, Britain and Japan. The following conclusions were drawn from this study: In terms of educational concept, the three countries follow the concept of inclusive education, and pursue equity and educational justice. They not only pay attention to inclusive education but also focus on improving the quality of education for students with disabilities. All three countries focus on accommodating children with special needs, but each implements its programs in a different way. These practices can be used as reference for the development of a special needs education law in China.

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.

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.

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.