Modification of the Conventional Influenza Epidemic Models Using Environmental Parameters in Iran

The association between the spread of infectious diseases and climate parameters has been widely studied in recent decades. In this paper, we formulate, exploit, and compare three variations of the susceptible-infected-recovered (SIR) model incorporating climate data. The SIR model is a well-studied model to investigate the dynamics of influenza viruses; however, the improved versions of the classic model have been developed by introducing external factors into the model.

The modification models are derived by multiplying a linear combination of three complementary factors, namely, temperature (T), precipitation (P), and humidity (H) by the transmission rate. The performance of these proposed models is evaluated against the standard model for two outbreak seasons.

The values of the root-mean-square error (RMSE) and the Akaike information criterion (AIC) improved as they declined from 8.76 to 7.05 and from 98.12 to 93.01 for season 2013/14, respectively. Similarly, for season 2014/15, the RMSE and AIC decreased from 8.10 to 6.45 and from 117.73 to 107.91, respectively. The estimated values of R(t) in the framework of the standard and modified SIR models are also compared.

Through simulations, we determined that among the studied environmental factors, precipitation showed the strongest correlation with the transmission dynamics of influenza. Moreover, the SIR+P+T model is the most efficient for simulating the behavioral dynamics of influenza in the area of interest.