Estimation of the Lubuma-Gumel Buffalo-only model with incomplete data

In this work, a reduced model proposed by Lubuma and Gumel for transmission dynamics of Mycobacterium tuberculosis and Bovine tuberculosis in a community consisting of humans and African buffaloes is considered. The buffalo-only component of the model is however, examined for parameter estimation. The problem is to propose an analytical approach for restoring the state variables, EB1 and EB2 which are the early and advanced-exposed buffaloes to Bovine tuberculosis respectively. These model variables are the assumed missing information about the population of susceptible Buffaloes. The discussed method is then used to restore this missing information in the susceptibles. The approach uses differential equations that are linearized through new parameters to form an objective function that is minimized using the least-squares methods in order to compute the required model coefficients. The Results show that the approach is efficient given the relatively small absolute errors - also the estimated trends that closely mimic the simulated (observed) data of the state variables.