KENDALI OPTIMAL MODEL PENYEBARAN PENYAKIT BLOOD DESEASE BACTERIUM (BDB) PADA TANAMAN PISANG KEPOK DENGAN INOKULASI BAKTERI ENDOFIT

Abstract

Banana plants are the most widely grown plants in Indonesia. In its growth period, banana plants can experience an attack of the disease Blood Desease Bacterium (BDB) caused by Ralstonia solanacearum Phylotipe IV which is the main cause of the loss of banana yield in Indonesia. BDB can cause plant death and crop failure. To represent this phenomenon a mathematical model was developed to reperents the spread BDB of Kepok banana plants by inoculating endophytic bacteria. Adapted 2 SEI epidemic models for banana and SI plant populations for the insect population trigona spp. The SEI model of banana population is divided into 3 subclasses, namely the BDB susceptible population class (𝑆ℎ), exposed population class (𝐸ℎ), and population class infected with BDB disease (𝐼ℎ). It was also observed the class of banana population that received treatment (𝑆𝑡 ). This group was a class of banana population that was given endophytic bacteria. The SI model was adapted for the insect population trigona spp. which are grouped into 2 subclasses, namely the vulnerable population class to infect BDB (𝑆𝑣 ), and the population class is ready to infect BDB (𝐼𝑣 ). Analysis of the stability of the model is carried out at a critical point then an optimal control of the spread of BDB disease through inoculation of endophytic bacteria is carried out. Controlling the rate of suppression of BDB transmission in bananas is done by keep the β parameters (isolates of endophytic bacteria inoculated into banana plants) for the purpose of reducing the incidence of BDB in banana plants. The simulation are carried out for optimal control design, using the principle of minimum Pontryagin, optimal solutions are obtained which show that controlling BDB disease with endophytic bacterial inoculation is said to be successful because it can reduce the number of infected banana plant populations.Keywords : BDB Disease, Endophytic bacteri, Inoculation, Ralstonia Solanacearum Phylotipe IV , Trigona spp., The Minimum Principle of Pontryagin.