A Dynamical Model for Transmission of West Nile Virus in Chicken-Mosquito Interaction

Jafaruddin^1,2, Juni Wijayanti Puspita³, Nuning Nuraini¹ & Edy Soewono^1
1Department of Mathematics, Institut Teknologi Bandung
Jalan Ganesha 10, Bandung 40132, Indonesia
²Department of Mathematics, Universitas Nusa Cendana
Jalan Adisucipto Kampus, Penfui, Kupang 80111, Nusa Tenggara Timur
³Department of Mathematics, Universitas Tadulako, Kampus Bumi Tadulako,
Jalan Soekarno-Hatta Km 9, Mauti Kolore, Palu Sulawesi Tengah 94118
Email: jafaruddin.hamid@yahoo.com

Abstract. The West Nile virus (WNV) is transmitted through the bites of infected mosquitoes. The spread of WNV in chicken populations is quite unique. Although chickens can contract the virus through a mosquito bite, they immediately build immunity to the virus and do not show physical symptoms of illness and hence chickens are only temporary carriers of the virus. Recently, experimental results have shown that mosquitoes do not change fecundity behavior, yet results indicate that resistance to infection is associated with a fitness cost in terms of mosquito survival. We constructed a host-vector type transmission model for WNV in mosquito-chicken populations. The basic reproductive ratio, , was obtained. From sensitivity analysis of it was shown that under certain conditions this ratio decrease – with an increase of the lifetime of mosquito infection. 

Keywords: basic reproductive ratio; dynamical model; mosquito-chicken interaction; stability analysis; WNV transmission.