Data
We used temperature data, rainfall data, and data on the incidence of malaria collected from 1901 to 2015 for 43 African countries to construct networks to determine the relationships between transmission of malaria and climate change elements, especially temperature and rainfall. Data resolution is given by the latitude and longitude of the capital city for every country in Africa. Temperature and rainfall data are provided in terms of monthly averages in the country wise. The nodes in the network represent the country, and the edges in the network represent the relationship between countries. We collected malaria data from Harvard Dataverse35 and the world malaria report from the WHO31. Data for temperature and rainfall were obtained from the Climate Change Knowledge Portal of the World Bank Group36.
Network generation and analysis
The networks were constructed by using the threshold method where the network depends on the mean, standard deviation, and the real number ((n)) used to control the features of the network. Therefore, data for temperature, rainfall, and the incidence of malaria were divided into six groups mostly comprising ranges of 20 years (1900–1920, 1921–1940, 1941–1960, 1961–1980, 1981–2000) as well as the period from 2001 to 2015. The missing data in Malaria incidence data are filled by the average amount of malaria incidence collected per year.
In Table S1, a malaria report from the World Health Organization shows that the rate of death is directly proportional to the incidence of malaria35. The death toll in Africa from malaria is about 98% of world deaths from malaria. Such deaths in African regions decrease thanks to efforts the WHO, governments, and the private sector have been conducting to prevent them. Weather and climate are among the factors that drive increases in malaria infections in different areas.
We consider networks based on the threshold method (see the “Methods and Materials” section below). First, we fill the missing malaria incidence data, and we calculate normalized Pearson correlation coefficients of three-time series between two countries. Then, we obtain a correlation matrix for the countries. We estimate the average value of the correlation coefficients from the time intervals 1901–1920, 1921–1940, 1941–1960, 1961–1980, 1981–2000, and 2001–2015 for three time series: temperature, rainfall, and incidence of malaria. We summarize the averages and standard deviations of the correlation coefficients, as shown in Table S2. The mean values from the correlation in temperature are high, compared to those for rainfall and the incidence of malaria. The standard deviations in temperature and rainfall are large, but the standard deviation for the incidence of malaria is small.
We chose an ad hoc threshold value of the correlation coefficients to generate sparse networks. The characteristic values for (n) of the threshold are given in Table S3. We consider three types of thresholds in order to observe changes in the networks according to the threshold.
Let us define the normalized variance of each time series. We considered time series (T_{i} left( t right)), (M_{i} left( t right)), and (R_{i} left( t right)) in country (i) for temperature, the incidence of malaria, and rainfall, respectively. We define normalized variance as
$$r_{ij} = frac{{x_{i} left( t right)x_{j} left( t right) – x_{i} left( t right)x_{j} left( t right)}}{{sigma_{i} sigma_{j} }}$$
(1)
where (x_{i} left( t right)) = (T_{i} left( t right)), (M_{i} left( t right)), (R_{i} left( t right)). We obtained a Pearson correlation matrix for each time series as follows:
$$R_{S} = left[ {begin{array}{*{20}c} {r_{11} } & cdots & {r_{1N} } vdots & {r_{ij} } & vdots {r_{N1} } & cdots & {r_{NN} } end{array} } right]$$
(2)
where (S = T, M, R).
We calculated the average value, (overline{r }), and the standard deviation, (sigma), for the correlation coefficients of the matrix. We applied the threshold method to generate a sparse network from the correlation matrix. Two countries are connected in the correlation network if and only if the value of the correlation coefficient is greater than, or equal to, the threshold value:
$$r_{{ij}} = left{ {begin{array}{*{20}c} 1 & {{text{if}};r_{{ij}} ge bar{r}{text{ + n}}sigma } 0 & {{text{otherwise}}} end{array} } right.$$
(3)
where (r_{ij}) is the correlation coefficient between two countries, and (n) is an element of real numbers ((n in {mathbb{R}})). The value of (n) determines whether the network is sparsely or densely connected.
We use Python programming language, packages, numpy for mathematical functions and random number generator, pandas for data analysis and manipulations, networkx for creation, manipulation, and studying the structure of the complex network, matplotlib for visualization and plotting graph and base map for map projection and visualization of geographic information.
Source: Ecology - nature.com
