GENERAL THEORY FOR SIGNIFICANCE OF CULLING IN TWO-WAY DISEASE TRANSMISSION BETWEEN HUMANS AND ANIMALS

An epidemic model is proposed to comprehend the disease dynamics between humans and animals and back to humans with a culling intervention strategy. The proposed model is separated into two cases with two different culling rates: (1) at a per-capita constant rate and (2) constant population being culled. The global asymptotic stability of equilibria is determined in terms of the basic reproduction numbers. Further, we find that the culling rate (2) considered in the model could change the dynamics by having multiple positive equilibria. Sensitivity analysis recommends developing a strategy that promotes animals’ natural and disease-related death rates. By ranking the efficacies of various intervention strategies, we obtain that vaccination in the human population, isolation and public awareness are the largely effective control interventions. Our general theory raises concerns about both human and animal populations becoming reservoirs of the disease and affecting each other dynamically.