ANALISIS KESTABILAN PADA MODEL PENYEBARAN PENYAKIT DEMAM DENGUE DENGAN MASA INKUBASI VIRUS DAN LAJU INSIDENSI NONLINEAR; STABILITY ANALYSIS OF DENGUE TRANSMISSION MODEL WITH THE INCUBATION PERIOD OF VIRUS AND NONLINEAR INCIDENCE RATE

I PUTU WINADA GAUTAMA, Widodo

2014 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

In this thesis, a mathematical model of transmission of dengue disease with nonlinear incidence rate and the length of time during incubation of dengue virus in human and mosquito is formulated. We assumed that the incidence rate for human population and mosquito population transmitted disease present, respectively, saturation and bilinear incidence rate. The existence of disease-free equilibrium, endemic equilibrium and its local stability is controlled by the threshold number. If the threshold number less than or equal to one, the disease-free equilibrium is globally asymptotically stable and the disease always dies out, if it exceeds one there will be an endemic. Numerical simulation is given to illustrate the results. Keywords: dengue disease, stability analysis, incubation period, basic reproduction number.

Kata Kunci : STABILITY ANALYSIS, DENGUE TRANSMISSION MODEL, INCUBATION PERIOD OF VIRUS, NONLINEAR INCIDENCE RATE