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Home  >  Volume 38

29. A Mathematical Model for Endemic Lassawith Constant Human and Rat Populations by Haruna M., Okeowo. G.F. & Idoko J.E. Volume 38, (November, 2016), pp 197 – 206
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Abstract

Lassa fever remains a regional health problem in some West African countries.The first case was isolated/discovered in a town called Lassa in Borno State, Nigeria in I969. The disease got its name from the name of the town. In this paper, we considered two components of transmission of Lassa fever infection: human and rat. We also adopt SIRS model for human and SI model for rat. Six ordinary differential equations were used to formulate our transmission model. We determined the Basic reproductive number, R_0 using Next Generation Method. Existence of disease-free equilibrium and endemic equilibrium were established. Using Jacobian method it was discovered that the disease free equilibrium is locally asymptotically stable when R_0<1. The disease free equilibrium is globally asymptotically stable when R_0<1, otherwise the disease free equilibrium is unstable. Using Lynapunov method it was discovered that the endemic equilibrium state is locally asymptotically stable when R_0>1, and using Jacobian function method it was discovered that the endemic equilibrium state is globally asymptotically stable when R_0>1 otherwise the endemic equilibrium is unstable. A Lassafever control measureswere incorporated into our model and this helped in controlling the transmission of Lassa fever infection. We carried out sensitivity analysis of our model and it was discovered thatthe infection impacts negatively on the model.

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