Analysis of SIS-SI Stochastic Model with CTMC on the Spread of Malaria Disease


  • Niswah Yanfa Nabilah Syams Department of Mathematics, Bogor Agricultural University, Jl. Meranti, Kampus IPB Dramaga, Bogor 16680, Indonesia
  • Hadi Sumarno Department of Mathematics, Bogor Agricultural University, Jl. Meranti, Kampus IPB Dramaga, Bogor 16680, Indonesia
  • Paian Sianturi Department of Mathematics, Bogor Agricultural University, Jl. Meranti, Kampus IPB Dramaga, Bogor 16680, Indonesia



basic reproduction number, expected time to reach disease-free equilibrium, malaria disease, outbreak probability, quasi-stationary distribution


Various mathematical models have been developed to describe the transmission of malaria disease. The purpose of this study was to modify an existing mathematical model of malaria disease by using a CTMC stochastic model. The investigation focused on the transition probability, the basic reproduction number (R0), the outbreak probability, the expected time required to reach a disease-free equilibrium, and the quasi-stationary probability distribution. The population system will experience disease outbreak if R0>1, whereas an outbreak will not occur in the population system if R0?1. The probability that a mosquito bites an infectious human is denoted as k, while ?is associated with human immunity. Based on the numerical analysis conducted, k and ?have high a contribution to the distribution of malaria disease. This conclusion is based on their impact on the outbreak probability and the expected time required to reach a disease-free equilibrium.


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