## MATHEMATICAL MODEL OF WEST NILE VIRUS WITH INFECTED IMMIGRANT BIRDS

Published: 2018-04-27

Page: 234-248

ABDUL, SUNDAY

Department of Mathematics, Kogi State College of Education, Ankpa, Nigeria.

PETER ENEMALI *

Department of Mathematics, Federal University of Agriculture, Makurdi, Benue State, Nigeria.

LEONARD PIUS OCHEUJE *

Department of Statistics, Central Bank of Nigeria, Abuja, Nigeria.

ALOYSIUS UGWUOKE *

Department of Mathematics, Federal University of Agriculture, Makurdi, Benue State, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

The complex task of controlling infectious diseases has long been assisted by mathematical modeling. Control and preventions of malaria, cholera, cancer and other diseases have been achieved by modeling. This research is on Mathematical Model of the West Nile Virus with infected Immigrant Birds. West Nile virus is a mosquito-borne flavivirus found in temperate and tropical regions of the world. Some obvious symptoms of infection with this virus include fever, headaches, fatigue, muscle pain or aches, malaise, nausea, anorexia, vomiting, myalgias and rash. In rare cases, West Nile virus can lead to inflammation of the brain (encephalitis), swelling of the spiral cord (myelitis), or swelling of the tissues around the brain and spinal cord (meningitis). The virus is transmitted majorly to female mosquitoes from infected birds. The infected mosquitoes could transmit the virus to man. This research work formulated a model to monitor the dynamics of the transfer of the west nile virus between birds and mosquitoes. The Model formulated is a non linear Ordinary Differential Equation. The model reveals that reduction of immigration of infected birds can reduce the peak of infection of the disease among birds. Numerical simulations however show that immigrant birds have no consequence on the total infected mosquito.

Keywords: Basic reproduction number, virus, equilibrium, local stability

#### How to Cite

SUNDAY, A., ENEMALI, P., OCHEUJE, L. P., & UGWUOKE, A. (2018). MATHEMATICAL MODEL OF WEST NILE VIRUS WITH INFECTED IMMIGRANT BIRDS. Asian Journal of Mathematics and Computer Research, 24(4), 234–248. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/1088

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