Eur. Phys. J. Plus (2020) 135:366 https://doi.org/10.1140/epjp/s13360-020-00357-0 Regular Article Dynamical features of pine wilt disease model with asymptotic carrier Muhammad Ozair 1 , Takasar Hussain 1 , Xiangyun Shi 2 , Fatima Tasneem 1 , J. F. Gómez-Aguilar 3,a 1 Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan 2 Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, People’s Republic of China 3 CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos, Mexico Received: 3 February 2020 / Accepted: 21 March 2020 / Published online: 21 April 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract The mathematical version for the transmission dynamics of pine wilt disease is explored, and its important mathematical features is analysed. Explicit formula for the reproduction number is calculated. Analytically, it is proved that the disease can be eradicated if the basic reproduction number becomes below unity. If this number exceeds unity, then a constant level of infectious and non-infectious classes is obtained. To explore the most influential factors for spread of the disease, we perform sensitivity analysis of the parameters. More interestingly, effective control programs have been designed on the basis of these sensitive parameters. Graphically, it has been shown that significant reduction has been occurred in the infected classes of pine trees by applying these controls. 1 Introduction Wilt diseases are the most common in angiosperms than gymnospermous types of trees. Two wilt diseases of pines have been identified up till now: one caused by the nematode Bur- saphelenchus xylophilus and other brought about blue-stain fungi of the genus Ceratocystis. It was first described in 1971 that Bursaphelenchus xylophilus is the only resource of pine wilt disease (PWD) of native pines in Japan [1]. Monochamus alternatus named as “pine sawyer beetle” is the vector for this parasite. The initial notable symptom of PWD is reduction in the emission of oleoresin from wounds of bark. Further indication is the conversion of needle colour. It becomes light grayish green to yellowish green, then yellowish brown and, lastly, fully brown when tree capitulates to the malady [2, 3]. Early occurrence of PWD goes back to 1905. During 1930s, the annual loss of pines increased from 30,000 m 3 to 200,000 m 3 , and during 1940s destructions were estimated at volumes of 400,000 m 3 every year. The struggle to overcome the malady was abandoned during World War II, which resulted in a expeditious increase in infected pine trees and immense loss of 1,230,000 m 3 in 1948. Considerable efforts lessened the annual loss to 400,000 m 3 during the 1950s. Elimination of dead trees by means of tumbling and blazing was a e-mail: jose.ga@cenidet.tecnm.mx (corresponding author) 123