A model of dengue fever

Abstract

Background: Dengue is a disease which is now endemic in more than 100 countries of Africa, America, Asia and the Western Pacific. It is transmitted to the man by mosquitoes (Aedes) and exists in two forms: Dengue Fever and Dengue Haemorrhagic Fever. The disease can be contracted by one of the four different viruses. Moreover, immunity is acquired only to the serotype contracted and a contact with a second serotype becomes more dangerous.

Methods: The present paper deals with a succession of two epidemics caused by two different viruses. The dynamics of the disease is studied by a compartmental model involving ordinary differential equations for the human and the mosquito populations.

Results: Stability of the equilibrium points is given and a simulation is carried out with different values of the parameters. The epidemic dynamics is discussed and illustration is given by figures for different values of the parameters.

Conclusion: The proposed model allows for better understanding of the disease dynamics. Environment and vaccination strategies are discussed especially in the case of the succession of two epidemics with two different viruses.

Figure 1

schematic diagram: compartments of human and vector populations

Figure 2

the role of reduction of susceptible humans (S_h) and mosquito population (N_v) to control the disease in the first and second epidemic (model without vaccination (ie p = 0)) S_h = 10000, N_v = 50000 S_h = 2000, N_v = 5000 S_h = 5000, N_v = 50000

Figure 3

the reduction of the mosquito population is not sufficient to eradicate dengue fever (model without vaccination (ie p = 0)) N_v = 50000 N_v = 30000 N_v = 800

Figure 4

The role of vaccination in the eradication of the disease in the first and second epidemic without vaccination (ie p = 0) p = 0.25 p = 0.75