DETERMINISTIC AND STOCHASTIC MODEL FOR THE TRANSMISSION OF LASSA FEVER
Abstract
Many models on the transmission dynamics of Lasser fever were based on purely deterministic approach. This approach does not put into cognizance randomness which is inherent in disease transmission resulting from differences in immunity levels, contact patterns, hygienic practices and mutation rates among so many other possibilities. In this work, we attempt to demonstrate the impact of uncertainties in the mode of transmission of Lassa fever by subjecting the dynamics to some white noise modeled by the Brownian motion as a Wiener process. An existing deterministic model involving the Susceptible, Exposed, Infected and Recovered (SEIR) individuals was transformed into a stochastic differential equation model by applying the procedure proposed by Allen et al (2008). The resulting system of Stochastic Differential Equations (SDE) was solved numerically using the Milstein scheme for SDEs. An algorithm for the method was developed and implemented in Python programming language. Numerical simulations of the model was done using four sets of parameters; , representing the natural birth rate, the natural death rate , the recovering rate from infected to recovered, transmission rate from exposed to infected ,transmission rate from susceptible to exposed are carried out to investigate the transmission dynamic of Lassa fever. The results of the simulations indicate that randomness does affect transmission of Lassa fever. We therefore recommend that factors such as social behavior, hygienic practices, contact patters, mutation rate should be considered while formulating mathematics models of disease transmission.
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