Healthc Inform Res.  2019 Jan;25(1):27-32. 10.4258/hir.2019.25.1.27.

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

Affiliations
  • 1Department of Health Information Management, School of Allied Medical Sciences, Tehran University of Medical Sciences, Tehran, Iran. niakan2@gmail.com
  • 2Department of Health Information Management, School of Allied Medical Sciences, Lorestan University of Medical Sciences, Khorramabad, Iran.

Abstract


OBJECTIVES
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.
METHODS
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.
RESULTS
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.
CONCLUSIONS
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.

Keyword

Epidemiology; Human Influenza; Least-Squares Analysis; Basic Reproduction Number; Climate

MeSH Terms

Basic Reproduction Number
Climate
Communicable Diseases
Epidemiology
Humidity
Influenza, Human*
Iran*
Least-Squares Analysis
Orthomyxoviridae
Seasons

Figure

  • Figure 1 Predictions using SIR and three modified models. Solid squares indicate the weekly number of infections from World Health Organization data. (A) Real-data and predictions in season 2013/14 for the standard model and its three modifications. (B) Real-data and predictions in season 2014/15 for the standard model and its three modified models. SIR: susceptible-infected-recovered, P: precipitation, T: temperature.

  • Figure 2 (A) AIC criteria for two influenza seasons 2013/14 and 2014/15. For both seasons, the SIR+P+T model has the lowest AIC. (B) RMSEs for the same influenza seasons. Similarly, the SIR+P+T model is the most rigorous model in term of RMSE. AIC: Akaike information criterion, RMSE: root-mean-square error, SIR: susceptible-infected-recovered, P: precipitation, T: temperature.

  • Figure 3 Residual error for SIR and SIR+P+T model for the two studied seasons of 2013/14 (A) and 2014/15 (B). The residual error values for the latter model (triangle) are obviously smaller than those of the standard model (asterisk). Also, the linear regression for both models, green and purple dashed lines, are represented for two seasons. The green and purple dashed lines correspond to null and the modified model, respectively. RMSE: root-mean-square error, SIR: susceptible-infected-recovered, P: precipitation, T: temperature.

  • Figure 4 Effective reproductive function R(t) for the SIR and SIR+P+T models. The green plot corresponds to the modified model in which R(t) lies in the interval [0.36, 2.10]; however, the purple graph lies in a wider interval. SIR: susceptible-infected-recovered, P: precipitation, T: temperature.


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