A Dynamical and Zero-Inflated Negative Binomial Regression Modelling of Malaria Incidence in Limpopo Province, South Africa

Abstract

Recent studies have considered the connections between malaria incidence and climate variables using mathematical and statistical models. Some of the statistical models focused on time series approach based on Box-Jenkins methodology or on dynamic model. The latter approach allows for covariates different from its original lagged values, while the Box-Jenkins does not. In real situations, malaria incidence counts may turn up with many zero terms in the time series. Fitting time series model based on the Box-Jenkins approach and ARIMA may be spurious. In this study, a zero-inflated negative binomial regression model was formulated for fitting malaria incidence in Mopani and Vhembe-two of the epidemic district municipalities in Limpopo, South Africa. In particular, a zero-inflated negative binomial regression model was formulated for daily malaria counts as a function of some climate variables, with the aim of identifying the model that best predicts reported malaria cases. Results from this study show that daily rainfall amount and the average temperature at various lags have a significant influence on malaria incidence in the study areas. The significance of zero inflation on the malaria count was examined using the Vuong test and the result shows that zero-inflated negative binomial regression model fits the data better. A dynamical climate-based model was further used to investigate the population dynamics of mosquitoes over the two regions. Findings highlight the significant roles of Anopheles arabiensis on malaria transmission over the regions and suggest that vector control activities should be intense to eradicate malaria in Mopani and Vhembe districts. Although An. arabiensis has been identified as the major vector over these regions, our findings further suggest the presence of additional vectors transmitting malaria in the study regions. The findings from this study offer insight into climate-malaria incidence linkages over Limpopo province of South Africa.

Keywords: Mopani; Vhembe; climate; dynamical models; malaria; zero inflated negative binomial regression.

Figure 1

Location of study area, showing (A) the malaria risk classification of South Africa and Kruger National Park; (B) the location of weather stations, the local municipalities and Mopani and Vhembe district municipalities, Limpopo province, South Africa.

Figure 2

Time series of daily temperatures over calibration period showing the (a) daily maximum and minimum temperature of Mopani district municipality, (b) daily maximum and minimum temperature of Vhembe district municipality Limpopo province, South Africa from January 1998 to December 2017.

Figure 3

Time series of daily climate variables and malaria cases over calibration period comparing the (a) daily average temperature, (b) rainfall and (c) malaria cases of Mopani and Vhembe district municipality, Limpopo province, South Africa from January 1998 to December 2017.

Figure 4

The barplot of malaria counts in Mopani and Vhembe district municipality, Limpopo province of South Africa.

Figure 5

Plot of autocorrelation function and partial autocorrelation function of residuals of ZINB model for Mopani and Vhembe district municipalities.

Figure 6

Plot of autocorrelation function and partial autocorrelation function of residuals of ZINB+ARIMA model for Mopani and Vhembe district municipalities.

Figure 7

Comparison between fitted and observed malaria count for Mopani District.

Figure 8

Comparison between fitted and observed malaria count for Vhembe District.

Figure 9

Scatter plot of daily simulated An. arabiensis and malaria cases over (a) Mopani and (b) Vhembe municipality, Limpopo province, South Africa from January 1998 to December 2017.