Tsutsugamushi disease, caused by a rickettsial bacteria known as Oriental tsutsugamushi, is one of the most febrile illnesses occurring throughout Korea during fall. O.tsutsugamushi is transmitted by the bite of infected, immature mites of the genus Leptotrombidium. The mites have four-stage life cycles : egg, larva, nymph, and adult. The larva is the only stage that can transmit the disease to humans and other vertebrates, since the other life stages do not feed on the host. During the process of obtaining a blood meal, they may either acquire the infection from the host or transmit the rickettiae to the other rodents or humans. The model can be divided the life cycle of mite into 2 stages : Larva and Adult. And the larva stage can be subdivided according to the phase of activity : questing and feeding. Mites enter either the susceptible questing larvae or infectious questing larvae through birth. When the larva bites an infectious hosts, then the larva moves from the susceptible questing to the infectious feeding class with some probability. On the other hand, hosts also enter the susceptible class through birth. And when an infectious larva bites a susceptible host, then the host enters the infectious class with some probability. In this talk, we introduce our mathematical model for the tsutsugamushi disease, and show the existence and stability condition of the disease-free equilibrium, which is a kind of threshold for the tsutsugamushi disease transmission, and also define the basic reproduction ratio R0. And we discuss about R0 related to all parameters.

• Byul Nim Kim(Laboratory of Mathematical and Computational Biology, Kyungpook National University)
• Yasuhisa Saito(Laboratory of Mathematical and Computational Biology, Kyungpook National University)
• Yongkuk Kim(Laboratory of Mathematical and Computational Biology, Kyungpook National University)