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# Malaria incidence and anopheles mosquito density in irrigated and adjacent non-irrigated villages of Niono in Mali

• * Corresponding author: Abdul-Aziz Yakubu
This research was supported by NSF under grants DMS 0931642 and 0832782.
• In this paper, we extend the mathematical model framework of Dembele et al. (2009), and use it to study malaria disease transmission dynamics and control in irrigated and non-irrigated villages of Niono in Mali. In case studies, we use our "fitted" models to show that in support of the survey studies of Dolo et al., the female mosquito density in irrigated villages of Niono is much higher than that of the adjacent non-irrigated villages. Many parasitological surveys have observed higher incidence of malaria in non-irrigated villages than in adjacent irrigated areas. Our "fitted" models support these observations. That is, there are more malaria cases in non-irrigated areas than the adjacent irrigated villages of Niono. As in Chitnis et al., we use sensitivity analysis on the basic reproduction numbers in constant and periodic environments to study the impact of the model parameters on malaria control in both irrigated and non-irrigated villages of Niono.

Mathematics Subject Classification: Primary:37C75, 92B05.

 Citation:

• Figure 1.  Niono in Mali (West Africa): Regions of both Irrigated and Non-irrigated Villages of Niono

Figure 2.  Human-Mosquito Dynamics in A Malaria Disease Transmission Model

Figure 3.  Periodic Mosquitoes Birth Rate in Both Regions $\lambda_m(t)\geq 0, \forall t \geq 0.$

Figure 4.  Periodic Mosquito Population: Dolo et al. Data Versus Model results

Figure 5.  Comparison of Malaria Incidences in Irrigated and Nonirrigated Villages

Figure 6.  Vectorial Capacity $C(t)$ in Both Irrigated and Non-irrigated Villages

Table 1.  Average Mosquito Population Densities per House in the Three Irrigated and the Three Adjacent Non-irrigated Villages

 Dates Apr. 96 Sep. 96 Jan. 97 Apr. 96 Oct. 97 Feb. 98 Non-irrigated 203 3,200.3 2 397 763 2.3 Irrigated 5,958 6,747 125.3 6,091.3 142 120

Table 2.  Total Human Populations in the Three Irrigated and the Three Adjacent Non-irrigated Villages

 Non-irrigated Irrigated $N_h$ $N_h$ 4,751 9,161

Table 3.  Model Parameters and Descriptions

 Regions Parameters Descriptions $\gamma$ Contact rate of humans-mosquitoes $\omega$ Angular velocity of the mosquito populations $\eta_m$ Progression rate from exposed (latent) to infected $g$ Duration of gonotrophic cycle Non-Irrigated/Irrigated $n$ Duration of extrinsic cycle of transmitted malaria parasite $\alpha$ Exposed rate of mosquitoes $\alpha_h$ Human recovery rate $\lambda$ Human birth/death rate $\beta$ Human loss of immunity rate $HBI$ Human blood index $p$ Mosquito probability of daily survival Non-Irrigated $\eta_h$ Infection rate of exposed human $\epsilon_d$ Mosquito death rate $HBI$ Human blood index $p$ Mosquito probability of daily survival Irrigated $\eta_h$ Infection rate of exposed human $\epsilon_d$ Mosquito death rate

Table 4.  Model Parameters and Values

 Regions Parameters Values in Days Source $\gamma$ $4\times10^{-1}/$day [8] $\omega$ $1.72\times10^{-2}/$day [Estimated] $\eta_m$ $8.3\times10^{-2}/$day [5] $g$ 2 days [11] Non-Irrigated/ $n$ 12 days [11] Irrigated $\alpha$ $4\times10^{-1}/$day [7] $\alpha_h$ $2.5\times10^{-1}/$day [7] $\lambda$ $10^{-4}/$day [7] $\beta$ $3\times10^{-2}/$day [7] $HBI$ $6.7\times 10^{-1}$ [12] $p$ $9.67\times 10^{-1}$ [7] Non-Irrigated $\eta_h$ $1.43\times10^{-1}/$day [Estimated][5] $\epsilon_d$ $3.3 10^{-2}/$day [7] $HBI$ $4.2\times 10^{-1}$ [12] $p$ $9.66\times 10^{-1}$ [Estimated] Irrigated $\eta_h$ $5.4\times10^{-2}/$day [Estimated][5] $\epsilon_d$ $3.4\times10^{-2}/$day [Estimated]

Table 5.  Values of $R_0^p$ for $\epsilon\in\left\{0, 0.2, 0.30, 0.35, 0.39\right\}.$

 Regions $\epsilon$ 0 0.2 0.3 0.35 0.39 Non-irrigated $R_0^p$ 2.22 2.2 2.18 2.17 2.16 Irrigated $R_0^p$ 4.65 4.61 4.57 4.54 4.52

Table 6.  Sensitivity Indices of $R_0.$

 Irrigated villages Non-irrigated villages Parameters Sensitivity index Parameters Sensitivity index $\eta_h$ $+0.00092$ $\eta_h$ $+0.00035$ $\lambda$ $-0.0011$ $\lambda$ $-0.00055$ $\epsilon_d$ $-0.69$ $\epsilon_d$ $-0.59$ $\eta_m$ $+0.145$ $\eta_m$ $+0.140$ $\alpha_h$ $-0.5$ $\alpha_h$ $-0.5$

Table 7.  Sensitivity Indices of $R_0^{p}.$

 Irrigated villages Non-irrigated villages Parameters Sensitivity index Parameters Sensitivity index $\eta_m$ $+0.29$ $\eta_m$ $+0.28$ $\eta_h$ $+0.0018$ $\eta_h$ $+0.0007$ $\lambda$ $-0.0022$ $\lambda$ $-0.0011$ $\alpha_h$ $-0.99$ $\alpha_h$ $-0.99$ $\epsilon_d$ $-1.38$ $\epsilon_d$ $-1.18$ $\epsilon$ $-0.047$ $\epsilon$ $-0.047$
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