An eco-epidemiological model with periodic transmission
In epidemiology or in eco-epidemiology, the mode of disease transmission is one of the most important factors, and the rate is highly influenced by seasonal factors like temperature, rainfall, humidity, etc. These environmental factors are likely to be of time periodic. Seasonality in effective contact rate is common in natural population, and less efforts are being paid so far on the eco-epidemiological systems. The present investigation aims at to study the dynamics by changing the constant transmission rate into periodic transmission rate. The basic reproduction number (R0) in periodic environment is analytically derived by spectral radius and thereby the conditions of the persistence, and the extinction of a disease are derived in terms of basic reproduction numbers. The conditions for existence of positive periodic solution and its global stability are also derived analytically. Numerical simulations are carried out to illustrate the analytical findings. Our main findings are that the periodic transmission rate plays an important role in the persistence and the recurrence of a disease in the population.