On dynamics of stochastic avian influenza model with asymptomatic carrier using spectral method
Asad Ali, Sami Ullah Khan, Ishtiaq Ali, Farman Ullah Khan
Abstract
In ecosystem, the most critical issue is the extinction and persistence of population. For this reason, various deterministic and stochastic models have been studied in the past decades. However, the effect of transitions which is caused by either internal or external environmental noise has given less attention. In this work, we introduce a robust and an efficient numerical scheme based on Legendre spectral collocation method (LSCM) to explore the asymptomatic behavior of stochastic influenza avian model. We consider the model in which both birds and human population are exposed class, while for the human population, the asymptomatic class is also considered, taking into account that the asymptomatic human beings may get re‐infected and migrate to symptomatic class. A fragmented treatment gives more consideration as they relocate symptomatic individuals towards the asymptomatic class. A generation approach is utilized to figure out the essential propagation number (called reproduction number) denoted by R 0 . For R 0 < 1, the system is asymptotically stable locally and has an ailment disease free equilibrium (DFE) and may have up to five endemic equilibria. Our simulations results recommend that the pace of complete predominance of influenza will be high, if all the individuals show symptoms upon infection and experience a deficient treatment. Further, the predominance pace of influenza is low, if all the individuals first move to symptomatic class and then treated effectively. An average rate of total prevalence is secured when more individuals upon disease move towards asymptomatic class. Our numerical simulations justified the theoretical results.