Modeling biological control of carrier-dependent infectious diseases

Since decades, hazardous chemicals are used to control the growth of carriers (flies, ticks, mites, and so on) in the environment, which are responsible for the spread of many infectious diseases, such as typhoid fever, polio, and some skin infections such as leprosy, and so on. Although these chemicals reduce the carrier population, they also inflict a sizeable harm to nontarget populations, like the human population. In this study, we present a mathematical model to control the carrier population using biological agents, which leads to the control of carrier-dependent infectious diseases. It is assumed that the disease can spread in the human population due to the direct contact between susceptible and infected individuals, but also indirectly through the vector population. The feasibility and stability of the system's equilibria are discussed. The key parameters of the proposed model are identified and their role in the transmission and control of such diseases is discussed. Our findings show that combined actions of two strategies, the biological control of carriers via parasitic wasps that target the immature stage of the flies and any extra exogenous means which eradicate the adult carriers when their population is at low levels, could be an effective and low cost approach to lessen the disease propagation.