Global dynamics for mathematical model of Echinococcus multilocularis in rodents and red foxes

A deterministic model for transmission of Echinococcus multilocularis (EM), a parasitic disease responsible for human alveolar echinococcosis, is formulated and analyzed rigorously. The model consists of two hosts, with three compartments each, and concentration of the parasites from environment as sources of infection. The model takes into account a predator-prey relationship between the major hosts and obtained a threshold value for their existence. Systematic derivation of basic reproduction number, R-0, is provided. Thorough qualitative analysis of the model reveals that it has a local and global asymptotic stable disease-free equilibrium when R-0 < 1; thus, (EM) will die out in the populations. However, when R-0 exceeds unity, the model exhibits a unique endemic equilibrium, which is globally asymptotic stable; hence, disease will persist. The elasticity indices and partial rank correlation coefficients of the basic reproduction number and cumulative new cases of the two hosts with respect to parameter values are computed. Sensitivity analyses identified key parameters that are the most sensitive and can be used for control strategies in reducing R-0 below unity. Numerical simulations are used to verify theoretical results and quantify prevalence of the disease in host populations.