Carlile Lavor

Improving methods for epidemiological control of canine visceral leishmaniasis based on a mathematical model. Impact on the incidence of the canine and human disease

The mathematical model described by Dye (1996) condemned the epidemiological canine visceral leishmaniasis control campaign, considering it non-efficient. Using this model, we mathematically demonstrate that the control is not efficient, only at low kappa values (rate at which latent and infectious dogs are lost by the destruction program) which match the canine seropositivity observed in the field by the immunofluorescency (IF) blood eluates analysis. With higher k values, corresponding to IF (kappa = 0.07) or ELISA (kappa = 0.25) results in sera samples, the number of infectious dogs declines to a Ro =1 or Ro =0, respectively, interrupting the transmission and the advancement of epidemics. We also experimentally demonstrate that the dog removal, following the results of IF of sera, instead of eluates lead to a 57% (p < 0.005) decrease in canine cases and 87.5% (p < 0.005) in human cases. Our mathematical and experimental results indicate that the control campaign become more efficient by enhancing the sensitivity of the diagnostic assay.

A Function to Test Methods Applied to Global Minimization of Potential Energy of Molecules

In this paper we develop a function with a functional form similar to general potential energy functions and whose global minimum is known. We prove that the number of local minimizers of this function increases exponentially with the size of the problem, which characterizes the principal difficulty in minimizing molecular potential energy functions. In order to guarantee the global optimality and to show the difficulty in obtaining the global minimum of this function, we propose the utilization of a deterministic algorithm. The algorithm is based on a branch and bound scheme that uses interval analysis techniques to calculate the lower bounds. Computational results for problems with up to 25 degrees of freedom are presented.