Abstract
Vector-borne diseases represent a threat to human and wildlife populations and mathematical models provide a means to understand and control epidemics involved in complex host-vector systems. The disease model studied here is a host-vector system with a relapsing class of host individuals, used to investigate tick-borne relapsing fever (TBRF). Equilibrium analysis is performed for models with increasing numbers of relapses and multiple hosts and the disease reproduction number, R0, is generalized to establish relationships with parameters that would result in the elimination of the disease. We show that host relapses in a single competent host-vector system is needed to maintain an endemic state. We show that the addition of an incompetent second host with no relapses increases the number of relapses needed for maintaining the pathogen in the first competent host system. Further, coupling of the system with hosts of differing competencies will always reduce R0, making it more difficult for the system to reach an endemic state.
Highlights
An important development in the study of infectious diseases is the application of mathematical models to understand the interplay between various factors that determine epidemiological processes
Vector-borne diseases are complex with interactions between multiple host and vector species
Understanding the transmission dynamics of vector-borne diseases is an important step towards controlling outbreaks and mitigating human infection risk
Summary
An important development in the study of infectious diseases is the application of mathematical models to understand the interplay between various factors that determine epidemiological processes. Vector-borne diseases are complex with interactions between multiple host and vector species [2,3,4]. Compartmental models, such as susceptible, infectious, and removed models (SIR) [5], have been applied to many disease systems in an effort to examine system dynamics. For some diseases, recovered individuals may relapse with a reactivation of infection and revert back to an infective class An example of such a system is found in van den Driessche et al [6], which included a relapsing rate between the susceptible and the same infected compartment. Noteworthy vector-borne relapsing diseases include tick-borne relapsing fever (TBRF) and malaria
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