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

Moussa Doumbia; Abdul-Aziz Yakubu

doi:10.3934/dcdsb.2017042

Article Contents

2017, Volume 22, Issue 3: 841-857. Doi: 10.3934/dcdsb.2017042

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

Moussa Doumbia^1, and
Abdul-Aziz Yakubu^2, ,

1.
Department of Mathematics, Howard University, Washington, DC 20059, USA
2.
Department of Mathematics, Howard University, Washington, DC 20059, USA

* Corresponding author: Abdul-Aziz Yakubu
* Corresponding author: Abdul-Aziz Yakubu

Received: July 31, 2015

Revised: August 31, 2016

Published: September 2017

This research was supported by NSF under grants DMS 0931642 and 0832782.

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Abstract

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.

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

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

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

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

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

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

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

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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

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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

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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

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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]

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

Regions	$ \epsilon $	0	0.20	0.30	0.35	0.39
Non-irrigated	$ R_0^p$	2.22	2.20	2.18	2.17	2.16
Irrigated	$ R_0^p$	4.65	4.61	4.57	4.54	4.52

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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 $	$\epsilon_d$	$-0.59$
$\eta_m$	$+0.145$	$\eta_m$	$+0.140$
$\alpha_h$	$-0.5$	$\alpha_h$	$-0.5$

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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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