# Climate Change and Vector-borne Diseases: An Economic Impact Analysis of Malaria in Africa

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Malaria and Its Link to Climate: An Overview

## 3. Model Specifications

_{it}is the natural log of the number of reported malaria cases per 1,000 people in country i at time period t; X

_{it}is a vector of climate variables that includes temperature, precipitation and a measure of climate variability; Z

_{it}is a vector of socio-economic control variables that includes population density, per capita gross domestic product, inequality index, per capita healthcare expenditure and number of hospital beds per 1,000 people; α

_{i}are unobserved individual country effects and u

_{it}is an idiosyncratic error term. The function f, the coefficients β and the unobserved country effects α

_{i}are all parameters to be estimated. Note that climate variables are assumed to affect the number of malaria cases per 1,000 people through an unknown function f to be estimated while the socio-economic variables affect malaria cases linearly.

## 4. Model Estimation

**Step1:**Express the conditional expectation of malaria cases per 1,000 people (y

_{it}) with respect to the climate variables (X

_{it}) as follows:

_{it}are assumed to be uncorrelated with the individual country effects and the idiosyncratic error terms. That is, climatic factors are uncorrelated to unobservable items that affect a particular country’s disease prevalence (e.g., poor environmental conditions, drug resistance) and the statistical error in fitting the model. This assumption allows consistent estimation of the linear parameters of the model. Note also that a measurement error on the number of cases is inevitable as many cases of malaria in remote area are unreported. However, it is well known in the econometric literature [33] that these measurement errors will not affect the consistency of our estimated coefficients.

_{it}= y

_{it}– Ê (y

_{it}|X

_{it}), Z̃

_{it}= [Z

_{it}– Ê(Z

_{it}|X

_{it})] and Ê(.|.)is a kernel estimator [28]. Equation (3) is then transformed into a well-known linear form:

_{it}and the country effects α

_{i}. The random effects specification assumes independence between Z̃

_{it}and the country effects α

_{i}. Since the independence between the individual unobserved effects and the regressors cannot be established ex ante, we use a Hausman specification test [35,36] to test the suitability of the fixed effects assumption. In this test the null hypothesis is that the individual unobserved effects and the regressors are uncorrelated (H

_{0}: E(α

_{i}|Z̃

_{it}) = 0).

**Step 2:**Given the estimates of β̂, then estimate the function using the relation

_{it}– β̂Z

_{it}= y̿

_{it}, we have the non-parametric form:

_{it}) = V′

_{it}θ (X

_{it}), where V

_{it}= (1, X

_{it}), we can estimate θ̂(X

_{it}) as:

## 5. Data

- Data on the country specific gini inequality index and area in square kilometers per country (used to compute the population density) are obtained from the CIA World Factbook [41].
- Per capita expenditures on health were obtained from the WHO report [14].
- Data on the number of hospital beds per 1,000 people were obtained from the Organization for Economic Cooperation and Development [42].

## 6. Empirical Model Specifications

_{0}) but also through the slope of temperature (θ

_{1}) and precipitation (θ

_{2}). That is, the effect of temperature and precipitation on the number of cases will depend on how precipitation variability evolves (consistent with the argument made by Jaenisch and Patz [25]). In other words, the size of the impact of temperature and precipitation on the malaria prevalence is conditioned by fluctuations in climate measured by the standard deviation in precipitation. The empirical statistical relationship between malaria cases, climatic and socio-economic variables can be written as:

_{l}, for l = 0,1,2 are smooth coefficients (or functions of climate variability) and β

_{k}are the coefficients of the linear socio-economic control variables. Note that in this specification the interaction between temperature and precipitation is established through the variability in precipitation.

## 7. Results and Their Interpretation

^{2}= 0.22) of the variations observed in the log of malaria cases per 1,000 people.

_{it}) = f (X

_{it}) + βZ

_{it}. The change in percentage of the number of malaria cases with respect to a one percent change in temperature or precipitation hereafter called elasticity is calculated as ${e}_{yx}=\frac{\partial y}{\partial x}\xb7\frac{x}{y}={\widehat{f}}^{\prime}(x){e}^{(\widehat{f}(x)+\widehat{\beta}z)}\xb7x/y$ and averaged over the 11 years period of study for each country.

## 8. Effects of Climate to Date and Projections

- the consequences of recent climate change on the observed malaria cases to date and
- the effects of projected climate change in 2080 to 2099 to cases that would be observed under those conditions.

## 9. Estimated Cost of Treatment for Future Cases

## 10. Conclusions and Discussion

## References

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**Figure 1.**Effect of climate variability (standard deviation of precipitation) on per capita malaria cases with 95% confidence intervals. This graph is the plot of the function θ

_{0}(STDPRECIP

_{it}) in Equation (8). It describes the impact of climate variability measured as the standard deviation of precipitation on malaria prevalence.

**Figure 2.**Effect of temperature levels on per capita malaria cases conditional on climate variability with 95% confidence intervals. This graph is the plot of the temperature function TEMP

_{it}* θ

_{1}(STDPRECIP

_{it}) in Equation (8). It shows how temperature levels affect malaria prevalence given the current climate variability conditions measured as the standard deviation in precipitation.

**Figure 3.**Effect of precipitation levels on per capita malaria cases conditional on climate variability with 95% confidence intervals. This graph is the plot of the precipitation function PRECIP

_{it}* θ

_{2}(STDPRECIP

_{it}) in Equation (8). It shows how temperature levels affect malaria prevalence given the current climate variability conditions measured as the standard deviation in precipitation.

Variable | Definition | Mean | Std. Dev. | Min. | Max. |
---|---|---|---|---|---|

CAPCASES | Malaria cases per 1,000 people. | 95.2 | 119.64 | 0.0 | 947.4 |

TEMP | Temperature (Degree Celsius) | 24.24 | 3.32 | 16.7 | 29.2 |

STDTEMP | Temperature standard deviation | 2.9 | 1.9 | 0.3 | 8.5 |

PRECIP | Precipitation (mm/m^{3}) | 777.4 | 479.3 | 37 | 1,921.7 |

STDPRECIP | Precipitation standard deviation | 60.0 | 41.1 | 1.3 | 220.4 |

POP | Population (million) | 18.5 | 22.1 | 0.5 | 118.9 |

POPDENS | Population Density per km^{2} | 51.5 | 59.3 | 1.9 | 304.6 |

CAPGDP | Per capita GDP(US$/capita) | 671.4 | 809.5 | 110.3 | 3,764.2 |

GINI | Gini inequality index | 42.9 | 7.2 | 29.8 | 61 |

CAPEXP | Health expenditure ($/capita) | 93.7 | 119.4 | 14 | 579 |

CAPBED | Hospital beds per 1,000 people. | 1.2 | 0.9 | 0.1 | 4.8 |

**Table 2.**Linear coefficient estimates (b).

Variables | Coefficients | Std. Dev. | T-Stats. | Other Stats. |
---|---|---|---|---|

CAPGDP | −0.0008 | 0.0004 | −1.86 ** | |

GINI | 0.3721 | 0.0821 | 4.53 * | |

POPDENS | 0.0001 | 0.0047 | 0.03 | |

CAPEXP | −0.0266 | 0.0056 | −4.71 * | |

CAPBED | 1.3648 | 0.4467 | 3.06 * | |

CONSTANT | 0.0321 | 0.0567 | 0.56 | |

Fisher-Stats (5,271) | 12.87 * | |||

R^{2} | 0.22 | |||

Hausman χ^{2} (5)-Stats (a) | 13.24 * |

^{*}significant at 1% critical level;

^{**}significant at 10% critical level.

^{(a)}The significance of the Hausman χ

^{2}statistic implies the rejection of the hypothesis of independence between the unobserved effects and the socio-economic variables. Therefore, the result presented in this table is obtained from fixed effects model specification.

^{(b)}Since the dependent variable is the log of malaria cases per 1,000 people, the linear coefficients could not be directly interpreted as marginal effects but for any regressor i the marginal effect should be calculated as β̂

_{i}* e

^{β̂Z}by using logarithmic functions derivative rule.

**Table 3.**Estimated change in the number of malaria cases due to climate change in the past 20 years (a).

Average annual cases per 1,000 people (1990–2000) | Cases Elasticity (%)
| Computed change in number of cases per 1,000 people under under observed climate change past 20 years | Equivalent percentage change per 1,000 people | ||
---|---|---|---|---|---|

to 1 º C change in Temp. | to 1% change in Precip. | ||||

Algeria | 0.01 | 155.25 | 2.38 | 0.00 | 0.33 |

Benin | 86.53 | 23.93 | −0.50 | −8.81 | −0.10 |

Botswana | 31.05 | 1.78 | −0.02 | 0.23 | 0.01 |

Burkina | 60.99 | 19.92 | −0.66 | −3.99 | −0.07 |

Burundi | 168.53 | 14.30 | 0.16 | 2.17 | 0.01 |

Central Afr. Rep. | 32.36 | −27.73 | 10.89 | 10.32 | 0.32 |

Chad | 45.14 | 0.87 | −0.15 | −0.12 | 0.00 |

Cote d'Ivoire | 55.56 | 183.91 | −13.69 | 8.25 | 0.15 |

Djibouti | 9.73 | 143.36 | 4.63 | 16.67 | 1.71 |

Egypt | 0.00 | 132.28 | 1.13 | 0.00 | 0.72 |

Ethiopia | 6.19 | −46.19 | −84.68 | −32.22 | −5.21 |

Ghana | 120.89 | 34.86 | −1.85 | −7.35 | −0.06 |

Guinea | 67.27 | −12.44 | −12.25 | −62.18 | −0.92 |

Malawi | 381.81 | 10.47 | −3.08 | 81.22 | 0.21 |

Mali | 27.40 | 11.59 | −0.01 | 0.64 | 0.02 |

Mauritania | 62.29 | 21.94 | 0.31 | 4.35 | 0.07 |

Morocco | 0.01 | 313.46 | 9.85 | 0.01 | 1.10 |

Niger | 96.78 | 14.84 | 0.23 | 7.38 | 0.08 |

Rwanda | 165.90 | 30.98 | −2.90 | 2.54 | 0.02 |

South Africa | 0.51 | 3.89 | 0.11 | 0.00 | 0.00 |

Sudan | 228.75 | 29.16 | −1.34 | −18.33 | −0.08 |

Togo | 112.28 | 8.37 | −0.23 | −4.43 | −0.04 |

Uganda | 92.24 | 4.39 | −0.32 | 2.23 | 0.02 |

Tanzania | 302.68 | 1.97 | 0.00 | 1.19 | 0.00 |

Zimbabwe | 98 | 12.65 | −0.53 | 2.68 | 0.03 |

^{(a)}The formula used to calculate the projected cases is based on the definition of elasticity. Let the elasticity value of the number malaria cases with respect to 1 °C change in temperature be a% and the elasticity value of the number of malaria cases with respect to 1% change in precipitation be b%. If the projected change in temperature in degree Celsius c

^{o}is and the projected change in precipitation is expressed in percentage as d%, then knowing the current number of malaria cases average m, the projected number of malaria cases is calculated as p = m × (a × c + b × d)/100.

Average annual cases per 1,000 people
| Cases Elasticity (%)
| Projected increase/decrease in cases per 1,000 people by the end of the Century (2080–2100) (a) | ||||
---|---|---|---|---|---|---|

(1990–2000) | to 1 ºC change in Temp. | to 1% change in Precip. | Scenario 1 | Scenario 2 | Scenario 3 | |

Algeria | 0.01 | 155.25 | 2.38 | 0.02 | 0.05 | 0.07 |

Benin | 86.53 | 23.93 | −0.50 | 41.17 | 67.48 | 90.42 |

Botswana | 31.05 | 1.78 | −0.02 | 1.14 | 1.91 | 2.61 |

Burkina | 60.99 | 19.92 | −0.66 | 25.49 | 39.28 | 50.66 |

Burundi | 168.53 | 14.30 | 0.16 | 42.55 | 79.01 | 110.41 |

Central Afr. Rep. | 32.36 | −27.73 | 10.89 | −47.88 | −22.56 | 14.23 |

Chad | 45.14 | 0.87 | −0.15 | 1.33 | 1.16 | 0.75 |

Cote d’Ivoire | 55.56 | 183.91 | −13.69 | 252.40 | 321.99 | 358.53 |

Djibouti | 9.73 | 143.36 | 4.63 | 23.77 | 47.80 | 71.26 |

Egypt | 0.00 | 132.28 | 1.13 | 0.01 | 0.01 | 0.01 |

Ethiopia | 6.19 | −46.19 | −84.68 | 10.57 | −45.82 | −143.26 |

Ghana | 120.89 | 34.86 | −1.85 | 96.03 | 134.58 | 162.20 |

Guinea | 67.27 | −12.44 | −12.25 | 59.12 | −44.10 | −171.21 |

Malawi | 381.81 | 10.47 | −3.08 | 217.00 | 182.96 | 121.42 |

Mali | 27.40 | 11.59 | −0.01 | 5.74 | 10.48 | 14.89 |

Mauritania | 62.29 | 21.94 | 0.31 | 22.84 | 45.49 | 67.35 |

Morocco | 0.01 | 313.46 | 9.85 | 0.04 | 0.10 | 0.16 |

Niger | 96.78 | 14.84 | 0.23 | 23.88 | 47.85 | 71.05 |

Rwanda | 165.90 | 30.98 | −2.90 | 106.97 | 130.78 | 100.65 |

RSA | 0.51 | 3.89 | 0.11 | 0.03 | 0.07 | 0.10 |

Sudan | 228.75 | 29.16 | −1.34 | 129.26 | 192.00 | 210.21 |

Togo | 112.28 | 8.37 | −0.23 | 19.25 | 30.49 | 40.00 |

Uganda | 92.24 | 4.39 | −0.32 | 8.17 | 10.88 | 10.00 |

Tanzania | 302.68 | 1.97 | 0.00 | 10.73 | 19.15 | 25.81 |

Zimbabwe | 97.53 | 12.65 | −0.53 | 29.66 | 0.00 | 4.84 |

^{(a)}The formula used to calculate the projected cases is based on the definition of elasticity. Let the elasticity value of the number malaria cases with respect to 1°C change in temperature be a% and the elasticity value of the number of malaria cases with respect to 1% change in precipitation be b%. If the projected change in temperature in degree Celsius is c° and the projected change in precipitation is expressed in percentage as d%, then knowing the current number of malaria cases average m, the projected number of malaria cases is calculated as p=m × (a × c + b × d)/100.

Price($) | Test($) | Transport($) | Total($) | |
---|---|---|---|---|

Drug prices | ||||

Artesunate | 0.54 | 1.39 | 0.48 | 2.41 |

Artesunate-Mefloquine | 0.36 | 1.39 | 0.44 | 2.18 |

Artemether-Lumefantrine | 0.15 | 1.39 | 0.38 | 1.92 |

Artesunate-Amodiquine | 0.08 | 1.39 | 0.37 | 1.83 |

Mean outpatient cost | 2.08 | |||

Hospitalization treatment cost | ||||

Kenya | 64.00 | |||

Senegal | 70.00 | |||

Mean Inpatient cost | 67.00 |

Projected cases per 1,000 people under Scenario1 | Treatment costs per 1,000 people (in 2004 USD)
| Treatment costs (in percentage of 2000 health expenditure per 1,000 people)
| |||
---|---|---|---|---|---|

Outpatient(a) | Inpatient(b) | Outpatient (%) | Inpatient (%) | ||

Algeria | 0.02 | 0.05 | 1.63 | 0.0 | 0.0 |

Benin | 41.17 | 85.76 | 2,758.58 | 0.3 | 8.1 |

Botswana | 1.14 | 2.36 | 76.08 | 0.0 | 0.0 |

Burkina | 25.49 | 53.08 | 1,707.60 | 0.1 | 3.2 |

Burundi | 42.55 | 88.63 | 2,851.00 | 0.6 | 20.4 |

Central Afr. Rep. | −47.88 | −99.73 | −3,208.11 | −0.2 | −6.4 |

Chad | 1.33 | 2.78 | 89.33 | 0.0 | 0.2 |

Cote d'Ivoire | 252.40 | 525.71 | 16,911.11 | 0.7 | 21.4 |

Djibouti | 23.77 | 49.50 | 1,592.37 | 0.1 | 2.5 |

Egypt | 0.01 | 0.01 | 0.35 | 0.0 | 0.0 |

Ethiopia | 10.57 | 22.02 | 708.40 | 0.1 | 3.7 |

Ghana | 96.03 | 200.02 | 6,434.28 | 0.2 | 6.3 |

Guinea | 59.12 | 123.14 | 3,961.17 | 0.2 | 5.2 |

Malawi | 217.00 | 451.96 | 14,538.70 | 1.1 | 35.5 |

Mali | 5.74 | 11.95 | 384.31 | 0.0 | 1.2 |

Mauritania | 22.84 | 47.58 | 1,530.61 | 0.1 | 4.8 |

Morocco | 0.04 | 0.09 | 2.87 | 0.0 | 0.0 |

Niger | 23.88 | 49.73 | 1,599.67 | 0.2 | 6.4 |

Rwanda | 106.97 | 222.79 | 7,166.67 | 0.7 | 22.4 |

South Africa | 0.03 | 0.06 | 2.06 | 0.0 | 0.0 |

Sudan | 129.26 | 269.22 | 8,660.18 | 0.7 | 21.7 |

Togo | 19.25 | 40.10 | 1,289.89 | 0.1 | 2.6 |

Uganda | 8.17 | 17.03 | 547.69 | 0.0 | 0.7 |

Tanzania | 10.73 | 22.35 | 718.98 | 0.1 | 2.9 |

Zimbabwe | 29.66 | 61.78 | 1,987.38 | 0.0 | 1.2 |

^{(a)}Average outpatient treatment costs are calculated by multiplying the number of projected malaria cases by the average drug prices in Table 5.

^{(b)}Average outpatient treatment costs are calculated by multiplying the number of projected malaria cases by the average hospitalization costs in Table 5.

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**MDPI and ACS Style**

Egbendewe-Mondzozo, A.; Musumba, M.; McCarl, B.A.; Wu, X.
Climate Change and Vector-borne Diseases: An Economic Impact Analysis of Malaria in Africa. *Int. J. Environ. Res. Public Health* **2011**, *8*, 913-930.
https://doi.org/10.3390/ijerph8030913

**AMA Style**

Egbendewe-Mondzozo A, Musumba M, McCarl BA, Wu X.
Climate Change and Vector-borne Diseases: An Economic Impact Analysis of Malaria in Africa. *International Journal of Environmental Research and Public Health*. 2011; 8(3):913-930.
https://doi.org/10.3390/ijerph8030913

**Chicago/Turabian Style**

Egbendewe-Mondzozo, Aklesso, Mark Musumba, Bruce A. McCarl, and Ximing Wu.
2011. "Climate Change and Vector-borne Diseases: An Economic Impact Analysis of Malaria in Africa" *International Journal of Environmental Research and Public Health* 8, no. 3: 913-930.
https://doi.org/10.3390/ijerph8030913