Translated Abstract
Dengue fever is an insect-borne highly pathogenic disease which is transmitted by Aedes mosquitoes,and it has outbroke many times in our country. The virus serotype is divided into four types, DEN-1, DEN-2, DEN-3, DEN-4, and each time we would see four serotypes when dengue outbroke, and every serotype will cause disease. Generally, the vaccine can only be effect for one type of dengue fever, and it is difficult to cure four serotypes, hence, it is difficult to achieve good vaccination effect. The recent outbreak of dengue fever lies in Guangdong in 2014,which involves a large number of people, causing significant economic losses. In this paper, we analyze the transmission and control of dengue fever in the view of epidemic dynamics.
Based on the general laws of the spread of infectious diseases,we established a constant coefficient dengue fever model spreading in Aedes and people. The novelty of the modeling idea is to divide the susceptible into two types,susceptibles who’s body contains antibodies and those not. The difference is that after being bitten by infectous Aedes, the former is far less chance getting infected than the latter. We calculated the basic reproduction number of the system,and we proved the global stability of the disease-free equilibrium when the basic reproduction number is less than unit. When the basic reproduction number is greater than unit, we obtain the existence and local stability of endemic equilibrium. Finally, we give the numerical simulation,and numerical simulations show that the number of susceptible individuals in the body is always zero, and the effects of the birth rate and mortality rate on the basic reproduction numbers are further studied.
Since the climatic factors such as temperature, rainfall and so on, which greatly affect the growth and density of Aedes mosquitoes, and the temperature as well as rainfall change periodically with time. Basing on the threshold theory of periodic system, we give definition of reproducing operator, and obtain the basic reproduction number. We give the disease-free periodic solution,and prove that when the basic reproductive number is less than unit, the disease-free periodic solution is stable. We prove that when the basic reproduction number is greater than unit,our system is persitent. The numerical simulation shows that the amplitude and phase of periodic infection rate and the growth rate of Aedes has an important effect on dengue fever.
Translated Keyword
[Basic reproductive number, Dengue fever model, Periodic solution, Stability]
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