SEIR Model of Dengue Hemorrhagic Fever with the Life Stage Structure of the Aedes albopictus Mosquito

Dengue Hemorrhagic Fever (DHF) is an acute febrile illness caused by the dengue virus. This virus belongs to group B arthropod-borne viruses (Arboviroses) of the genus Flavivirus, which has four serotypes, namely Dengue I, Dengue II, Dengue III, and Dengue IV. Dengue virus is transmitted by Aedes sp. The SEIR model studied places the Aedes albopictus mosquito as the main vector. Many DHF cases are caused by this mosquito because it has a larger coverage area and is more difficult to control. All Aedes mosquito species have four life stages, namely: (1) egg, (2) larva, (3) pupa, and (4) adult. A stage-structured model was chosen because Ae. albopictus has varying rates of development and mortality at different stages. This model study includes determining the fixed point, determining the basic reproduction number R0, analyzing the stability of the fixed point, and simulating the population dynamics of dengue virus transmission. This model indicates the presence of endemics in an area for certain parameter values. This model produces a disease-free equilibrium, or DFE, which will be stable when R0 < 1, otherwise unstable when R0 > 1. The dynamic results for each human population (susceptible, exposed, infected, and cured) through observations in numerical simulations are influenced by the selection of the R0 value. The value of R0 is influenced by the mosquito death rate parameter and the average bite rate of infected mosquitoes. Population dynamics simulations show that an increase in the death rate of mosquitoes will reduce the number of humans exposed to them. In addition, an increase in the average number of infected mosquito bites will increase the number of humans exposed. Changes in the number of humans in each population tend to be different for each increase in the mosquito mortality rate or for each increase in the average number of infected mosquito bites.