Modelo matemático para dispersão de leptospirose em rebanhos bovinos infectados pela sorovariedade Hardjo: transmissão e opções de controle

Abstract

The mathematical model SIRS (Susceptible - Infected - Recovered - Susceptible) for leptospirosis was proposed to simulate the dynamics of the disease in dairy cattle herd, infected with serovar Hardjo, analyzing different model parameters and immunization coverage. A system of differential equations was used to describe the transmission of the disease with the aid of ModelMaker4® software. The effect of the SIRS model dynamics incorporating immunization is presented in the simulation for different vaccination rates as a control measure for bovine leptospirosis, considering a six-month vaccine immunity for monovalent Hardjo vaccine and a four-month immunity for polyvalent vaccine. Sensitivity analysis was made for the following parameters: p (proportion of immunization coverage), (rate of transmission by direct contact) to investigate situations of prevalence and disease eradication and for the simulation of different immunization coverage for leptospirosis. For a value of = 1.0, with a 100% immunization coverage and a 100% vaccine efficiency, the eradication period of the disease was 190 years. With = 0.2, the eradication of the disease occurs and, consequently, the number of infected and recovered tends to zero. The compartmental SIRS model was effective to describe the dynamics of leptospirosis over time in a bovine herd of dairy cattle infected with serovar Hardjo.