Mathematical Global Dynamics and Control Strategies on Echinococcus multilocularis Infection.

Echinococcus multilocularis, a major cause of echinococcosis in human, is a parasitic sylvatic disease between two major hosts in a predator-prey relation. A new model for the transmission dynamics of Echinococcus multilocularis in the population of red foxes and voles with environment as a source of infection is formulated and rigorously analyzed. The model is used to access the impact of treatment on red foxes and environmental disinfection as control strategies on the disease dynamics. The control reproduction number is computed and is used to rigorously prove the local and global dynamics of models' equilibria. Using available data on Echinococcus, elasticity indices and partial rank correlation coefficients of control reproduction number and cumulative new cases in red foxes and voles are computed. Parameters that have high influence locally and globally are identified. Numerical experiments indicate that administering disinfection of environment only induces more positive impact than applying treatment only on red foxes in controlling the infection. Generally, interventions towards treating red foxes and environmental disinfection could be sufficient in tackling transmission of disease in the populations.

Analysis of a model of gambiense sleeping sickness in humans and cattle.

Human African Trypanosomiasis (HAT) and Nagana in cattle, commonly called sleeping sickness, is caused by trypanosome protozoa transmitted by bites of infected tsetse flies. We present a deterministic model for the transmission of HAT caused by Trypanosoma brucei gambiense between human hosts, cattle hosts and tsetse flies. The model takes into account the growth of the tsetse fly, from its larval stage to the adult stage. Disease in the tsetse fly population is modeled by three compartments, and both the human and cattle populations are modeled by four compartments incorporating the two stages of HAT. We provide a rigorous derivation of the basic reproduction number R0. For R0 < 1, the disease free equilibrium is globally asymptotically stable, thus HAT dies out; whereas (assuming no return to susceptibility) for R0 >1, HAT persists. Elasticity indices for R0 with respect to different parameters are calculated with baseline parameter values appropriate for HAT in West Africa; indicating parameters that are important for control strategies to bring R0 below 1. Numerical simulations with R0 > 1 show values for the infected populations at the endemic equilibrium, and indicate that with certain parameter values, HAT could not persist in the human population in the absence of cattle.