Mathematical Model of the Transmission Dynamics of Lassa Fever with Separation of Infected Individual and Treatment as Control Measures
S. C. Nwasuka *
Department of Mathematics and Statistics, Clifford University, Owerrinta, Abia State, Nigeria.
I. E. Nwachukwu
Department of Mathematics and Statistics, Clifford University, Owerrinta, Abia State, Nigeria.
P. C. Nwachukwu
Department of Biological Science, Clifford University, Owerrinta, Abia State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
A non–linear deterministic mathematical model is formulated and analysed to study the controllability of lassa fever incorporating separation of infected individuals and treatment measures. The model assumes that humans susceptible acquired the Infection via interaction with the infected rodent populations at a constant rate and also the model assumes that treatment is only given to separated human population. The existence, uniqueness and positivity of the model’s solution have been carried out and the results shows that the solution exist and is unique. Again, the disease – free equilibrium state was obtained and analysed. We obtained an important threshold parameter called the effective reproduction number using the next generation method. If Reff < 1 the disease-free equilibrium exists and is locally and globally asymptotically stable, implying that Lassa fever can be controlled and eradicated within the population in a finite time and if the , the disease invade and become endemic in the population.
Keywords: Lassa fever, mathematical model, separation of infected human, treatment, existence