Jicai Huang

Bifurcations of Invariant Tori in Predator-Prey Models with Seasonal Prey Harvesting

In this paper we study bifurcations in predator-prey systems with seasonal prey harvesting. First, when the seasonal harvesting reduces to constant yield, it is shown that various kinds of bifurcat...

MULTIPLE BIFURCATIONS IN A PREDATOR–PREY SYSTEM OF HOLLING AND LESLIE TYPE WITH CONSTANT-YIELD PREY HARVESTING

The bifurcation analysis of a predator–prey system of Holling and Leslie type with constant-yield prey harvesting is carried out in this paper. It is shown that the model has a Bogdanov–Takens singularity (cusp case) of codimension at least 4 for some parameter values. Various kinds of bifurcations, such as saddle-node bifurcation, Hopf bifurcation, repelling and attracting Bogdanov–Takens bifurcations of codimensions 2 and 3, are also shown in the model as parameters vary. Hence, there are different parameter values for which the model has a limit cycle, a homoclinic loop, two limit cycles, or a limit cycle coexisting with a homoclinic loop. These results present far richer dynamics compared to the model with no harvesting. Numerical simulations, including the repelling and attracting Bogdanov–Takens bifurcation diagrams and corresponding phase portraits, and the existence of two limit cycles or an unstable limit cycle enclosing a stable multiple focus with multiplicity one, are also given to support the theoretical analysis.

Bifurcation of Codimension 3 in a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response

It was shown in [Li & Xiao, 2007] that in a predator–prey model of Leslie type with simplified Holling type IV functional response some complex bifurcations can occur simultaneously for some values of parameters, such as codimension 1 subcritical Hopf bifurcation and codimension 2 Bogdanov–Takens bifurcation. In this paper, we show that for the same model there exists a unique degenerate positive equilibrium which is a degenerate Bogdanov–Takens singularity (focus case) of codimension 3 for other values of parameters. We prove that the model exhibits degenerate focus type Bogdanov–Takens bifurcation of codimension 3 around the unique degenerate positive equilibrium. Numerical simulations, including the coexistence of three hyperbolic positive equilibria, two limit cycles, bistability states (one stable equilibrium and one stable limit cycle, or two stable equilibria), tristability states (two stable equilibria and one stable limit cycle), a stable limit cycle enclosing a homoclinic loop, a homoclinic loop...

AVIAN INFLUENZA A H7N9 VIRUS HAS BEEN ESTABLISHED IN CHINA

In March 2013, a novel avian-origin influenza A H7N9 virus was identified among human patients in China and a total of 124 human cases with 24 related deaths were confirmed by May 2013. From November 2013 to July 2017, H7N9 broke out four more times in China. A deterministic model is proposed to study the transmission dynamics of the avian influenza A H7N9 virus between wild and domestic birds and from birds to humans, and is applied to simulate the open data on numbers of the infected human cases and related deaths reported from March to May 2013 and from November 2013 to June 2014 by the Chinese Center for Disease Control and Prevention. The basic reproduction number ℛ0 is estimated and sensitivity analysis of ℛ0 in terms of model parameters is performed. Taking into account the fact that it broke out again from November 2014 to June 2015, from November 2015 to July 2016, and from October 2016 to July 2017, we believe that H7N9 virus has been well established in birds and will likely cause regular outbr...

Modeling the Transmission Dynamics of Clonorchiasis in Foshan, China

Clonorchiasis, known as the Chinese liver fluke disease, is caused by Clonorchis sinensis infection with food-borne liver fluke, which is transmitted via snails to freshwater fish and then to human beings or other piscivorous mammals. Clonorchis sinensis infection is mainly related to liver and biliary disorders, especially cholangiocarcinoma, and has an increased human-health impact due to the greater consumption of raw freshwater fish. In this article, we propose a deterministic model to describe the spread of clonorchiasis among human-snail-fish populations and use the model to simulate the data on the numbers of inspected and infected individuals of Foshan City, located in Guangdong Province in the southeast of P.R China, from 1980–2010. Mathematical and numerical analyses of the model are carried out to understand the transmission dynamics of clonorchiasis and explore effective control measures for the local outbreaks of the disease. We find that (i) the transmission of clonorchiasis from cercariae to fish plays a more important role than that from eggs to snails and from fish to humans; (ii) As the cycle of infection-treatment-reinfection continues, it is unlikely that treatment with drugs alone can control and eventually eradicate clonorchiasis. These strongly suggest that a more comprehensive approach needs to include environmental modification in order to break the cercariae-fish transmission cycle, to enhance awareness about the disease, and to improve prevention measures.