MEMBANGUN MODEL PENYEBARAN PENYAKIT AKIBAT ASAP KEBAKARAN HUTAN

Abstract

Forest fires impact a very serious problem because it could cause health problem, especially respiratory disease such as (ISPA), Asthma and Bronchitis. The study of the health disorders is conducted by consider mathematicaly the spread of disease due to forest fires smoke. The model is constructed by devide the human population into six subpopulations, that is vulnerable S(t), exposed E(t), Asthma infected A(t), Bronchitis infected B(t) and recovered R(t).The governed model is analyted at every critical points using Routh-Hurwitz method. The results gives two critical points that describe a free disease conditions ( ) and an endemic conditions ( ). A stabil ( ) is occured if  and  where the threshold point of the stability is expressed as  and   . Endemic conditions  will be asymptotically stable when  and  with  . The condition of free disease of forest fires is occured in a long time period, while the endemic conditions is occurred in a short time period. It could be interpreted that the disease spread due to the forest fires smoke is not easy to overcome.