Abstract
In 2008 there was a large outbreak of Chikungunya f ever in the south of Thailand. Chikungunya fever is a febrile disease transmitted to humans by the bite o f infected Aedes mosquitoes. The symptoms of this disease are a sudden onset of a fever, chills, head ache, nausea, vomiting, joint pain with or without swelling, low back pain and rash. In this study we study the effects of there being two species of Aedes mosquito (Aedes aegypti and Aedes albopictus ) present. In this study, we assume that both the h uman and mosquito populations are constant. A dynamical model of Chikungunya fever is proposed and analyzed. The RouthHurwitz criteria are used to determine the stabilit y of the model. The conditions which would lead to either the disease free equilibrium state or the disease endem ic equilibrium state to exist is determined. The nu merical simulations are done in order to illustrate the beh aviors of transmission of disease for different val ues of parameters. It is shown that the destruction of bre eding sites could be an effective method to control this disease.
Highlights
Poletti et al (2011) developed a model describing the temporal (CHIKV) is transmitted to humans by the bite of an dynamics of the vector depending on climate factors, infected Aedes mosquito, widespread in some tropical coupled to an epidemic transmission model describing the Corresponding Author: Surapol Naowarat, Department of Mathematics, Faculty of Science and Technology, Suratthani Rajabhat University, Surat Thani, 84100, Thailand
The human population is divided into the susceptible human (Sh ), the infected human (Ih ) and the recover human population (Rh ) compartment
We change the value of the recruitment rate of mosquito to A1 = 5,000, A2 = 10,000 and keep the other values of parameters to be those given in Table 1, we find the eigenvalues to be λ1 = -0.6285525, λ2 = 0.186016, λ3 = -0.0283579, λ4 = -0.004557 and the basic reproductive number to be R0 = 4571.01>1
Summary
The cumulative number of notified cases predicted by the model was 185 on average, in good agreement with observed data. They found that the basic reproduction number was in the range of 1.8-6. Yakob and Clements (2013) proposed a simple model of the virus transmission between humans and mosquitoes. This model is fitted with data from Reunion epidemic, with basic reproductive number is 4.1. Numerical results showed the impact of the geographical environment and populations’ mobility on the spread of the disease
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