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The existence of positive periodic solutions of an eco-epidemic model with impulsive birth. (English) Zbl 1170.34034
The paper deals with an epidemiological predator-prey model with periodic coefficients and impulsive birth, where the predator population is split into two groups, susceptible and infected. Sufficient conditions for existence of at least one positive periodic solution are derived by using Mawhin’s coincidence degree for $L$-compact mappings. The authors claim that the conditions are easily verifiable, although applications are not discussed in the paper. The conclusion “we can protect the infected predator from extinction by periodically changing the periodic environmental factors, such as, the period of birth, and then prevent the predator from increasing” sounds unfounded from the biological point of view.
##### MSC:
 34C60 Qualitative investigation and simulation of models (ODE) 47N20 Applications of operator theory to differential and integral equations 34A37 Differential equations with impulses 34C25 Periodic solutions of ODE 92D25 Population dynamics (general) 92D30 Epidemiology