In this paper, we introduce and analyze two structured models for the transmission of a vector-borne infectious disease. The first of these models assumes that the level of contagiousness and the rate of removal (recovery) of infected individuals depends on the infection age. In the second model the hosts population is structured with respect to the physical age of the hosts, and the susceptibi...

Two systematic methods are presented to guide the construction of Lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics. Specifically, a matrix-theoretic method using the Perron eigenvector is applied to prove the global stability of the disease-free equilibrium, while a graph-theoretic method based on Kirchhoff’s matrix tree theorem...

A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. ...

This paper presents a novel mathematical model with multidrug-resistant MDR and undetected TB cases. The theoretical analysis indicates that the disease-free equilibrium is globally asymptotically stable if R0 < 1; otherwise, the system may exist a locally asymptotically stable endemic equilibrium. The model is also used to simulate and predict TB epidemic in Guangdong. The results imply that o...

We characterized 24 polymorphic tetranucleotide microsatellite loci for delta smelt (Hypomesus transpacificus) endemic to the San Francisco Bay Estuary, CA, USA. Screening of samples (n = 30) yielded two to 26 alleles per locus with observed levels of heterozygosity ranging from 0.17 to 1.0. Only one locus deviated from Hardy-Weinberg equilibrium, suggesting these individuals originate from a s...

In order to investigate the transmission mechanism of the infectious individual with Ebola virus, we establish an SEIT (susceptible, exposed in the latent period, infectious, and treated/recovery) epidemic model. The basic reproduction number is defined. The mathematical analysis on the existence and stability of the disease-free equilibrium and endemic equilibrium is given. As the applications...

An SIR model with distributed delay and a general incidence function is studied. Conditions are given under which the system exhibits threshold behaviour: the disease-free equilibrium is globally asymptotically stable if R0 is less than 1 and globally attracting if R0=1; if R0 is larger than 1, then the unique endemic equilibrium is globally asymptotically stable. The global stability proofs us...

Abstract. We formulate a delayed SIR epidemic model by introducing a latent period into susceptible, and infectious individuals in incidence rate. This new reformulation provides a reasonable role of incubation period on the dynamics of SIR epidemic model. We show that if the basic reproduction number, denoted, R0, is less than unity, the diseasefree equilibrium is locally asymptotically stable...

This article concerns the SIRC epidemiological model for influenza A, which efficiently describes the mechanism of disease spreading, including the susceptible (S), the infected (I) and the recovered (R), along with a crossimmune class (C) that recovers after being inflected by different strains of the same viral subtype. The dynamics of the model is completely determined by the basic reproduct...

In this paper, an SEIV epidemic model with vaccination and nonlinear incidence rate is formulated. The analysis of the model is presented in terms of the basic reproduction number R0. It is shown that the model has multiple equilibria and using the center manifold theory, the model exhibits the phenomenon of backward bifurcation where a stable diseasefree equilibrium coexists with a stable ende...