Modeling and analyzing the effects of fixed-time intervention on transmission dynamics of echinococcosis in Qinghai province

In this study, we propose a mathematical model with periodic transmission and impulsive interventions to describe the transmission dynamics of echinococcosis in multiple hosts and to explore the efficacy of control and prevention measures. Our model includes the life cycle of Echinococcus in dog population (stray dogs and domestic dogs), contaminated environment, and human population to gain new biological insight. Note that different control strategies on stray and domestic dog populations may lead to inconsistency in the impulsive periods and system itself period, which brings great challenges in analyzing the proposed periodic system with multiple pulses. We theoretically examined the threshold dynamics, uniform persistence of disease on the basis of basic reproduction number. In particular, we define the basic reproduction number for stray and domestic dog population and obtain the globally asymptotical stability of the disease-free periodic solutions. We further obtain that echinococcosis may persist in human population if it persists in any dog population. Numerical simulations show that increasing the delivery rate and frequency of anthelmintics in domestic dogs and increasing the culling intensity and frequency in wild dogs could greatly reduce the disease incidence in two populations, respectively. The findings suggest that culling measures on wild dog population and environmental hygiene are crucial strategies in the control of the spread of echinococcosis in human being.