Abstract
Migratory birds are critical to the prevalence of many epidemic diseases. In this paper, a new two species eco-epidemiological model with disease in the migratory prey is formulated. A modified Leslie-Gower functional scheme, with saturated incidence and recovery rate are considered in this new model. Through theoretical analysis, a series of conditions are established to ensure the extinction, permanence of the disease, and to keep the system globally attractive. It was observed that if the lower threshold value $R_{*}>1$ , the infective population of the periodic system is permanent, whereas if the upper threshold value $R^{*}\leq1$ , then the disease will go to extinction. Our results also show that predation could be a good choice to control disease and enhance permanence.
Highlights
Nowadays, an important issue in applied mathematics is to study the influence of epidemiological parameters on ecological systems
Let β(t) = . + . sin t and retain the other parameter values as in Figure, we can see that the two upper threshold values are R∗ = .
Changing the infection rate from β(t) = . + . sin t to β(t) = . + . sin t, we have the upper threshold values R∗ = . and R∗ = . , respectively, which are greater than, by Figure (a)-(b), it can be seen that the infected prey population is permanent
Summary
An important issue in applied mathematics is to study the influence of epidemiological parameters on ecological systems. In Section , we analyze the nonautonomous differential equations for migratory birds and establish a set of sufficient conditions to discuss the extinction, the permanence of the disease, and keep the system globally attractive. M , we can obtain the theorem about the permanence of the infective prey population as follows. Under assumptions (B ), (B ), (B ), if there exist constants λ > and ω > satisfying t+λ lim inf β(θ )S (θ ) – e(θ ) – f (θ ) – c (θ )p (θ )
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
