May 2017, 22(3): 841-857. doi: 10.3934/dcdsb.2017042

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

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

Received  August 2015 Revised  September 2016 Published  January 2017

Fund Project: 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.

Citation: Moussa Doumbia, Abdul-Aziz Yakubu. Malaria incidence and anopheles mosquito density in irrigated and adjacent non-irrigated villages of Niono in Mali. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 841-857. doi: 10.3934/dcdsb.2017042
References:
[1]

R. AguasL. J. WhiteR. W. Snow and M. G. M. Gomes, Prospects for malaria eradication in Sub-Saharan Africa, PLoS ONE., 3 (2008), e1767.

[2]

S. AkbariN. K. Vaidya and L. M. Wahl, The time distribution of sulfadoxine-pyrimethamine protection from malaria, Bulletin of Mathematical Biology, 74 (2012), 2733-2751.

[3]

N. Bacaer, Approximation of the basic reproduction number R0 for vector-borne diseases with a periodic vector population, Bulletin of Mathematical Biology, 69 (2007), 1067-1091. doi: 10.1007/s11538-006-9166-9.

[4]

J. -F. Belieres, L. Barret, Z. Charlotte Sama and M. Kuper, https://hal.archives-ouvertes.fr/cirad-00190904/document

[5]

http://www.cdc.gov/malaria/about/disease.html.

[6]

N. ChitnisJ. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of Mathematical Biology, 70 (2008), 1272-1296. doi: 10.1007/s11538-008-9299-0.

[7]

B. DembeleA. Friedman and A. A. Yakubu, Mathematical model for optimal use of sulfadoxine-pyrimethamine as a temporary malaria vaccine, Bulletin of Mathematical Biology, 72 (2010), 914-930. doi: 10.1007/s11538-009-9476-9.

[8]

B. DembeleA. Friedman and A. A. Yakubu, Malaria model with periodic mosquito birth and death rates, Journal of Biological Dynamics, 3 (2009), 430-445. doi: 10.1080/17513750802495816.

[9]

K. Dietz, Mathematical models for malaria in different ecological zones, Biometrics 27 808 17TH ST NW Suite 200, Washington, DC 20006-3910: International Biometric Soc. , 1971.

[10]

K. DietzW. H. Wernsdorfer and I. McGregor, Mathematical models for transmission and control of malaria, Malaria: Principles and Practice of Malariology, 2 (1988), 1091-1133.

[11]

M. A. Diuk-Wasser, Vector abundance and malaria transmission in rice-growing villages in Mali, The American Journal of Tropical Medicine and Hygiene, 72 (2005), 725-731.

[12]

G. Dolo, Malaria transmission in relation to rice cultivation in the irrigated Sahel of Mali, Acta Tropica, 89 (2004), 147-159.

[13]

E. E. Frances, Survivorship and distribution of immature Anopheles gambiae sl (Diptera: Culicidae) in Banambani village, Mali, Journal of Medical Entomology, 41 (2004), 333-339.

[14]

N. J. GovellaF. O. Okumu and G. F. Killeen, Insecticide-treated nets can reduce malaria transmission by mosquitoes which feed outdoors, The American Journal of Tropical Medicine and Hygiene, 82 (2010), 415-419.

[15]

G. F. KilleenA. Seyoum and B. G. J. Knols, Rationalizing Historical successes of malaria control in Africa in terms of mosquito resource availability management, The American Journal of Tropical Medicine and Hygiene, 71 (2004), 87-93.

[16]

F. Lardeux, Host choice and human blood index of Anopheles pseudopunctipennis in a village of the Andean valleys of Bolivia-art. no. 8, Malaria Journal, 6 (2007), NIL1-NIL1.

[17]

G. Macdonald, The analysis of infection rates in diseases in which super infection occurs, Tropical Diseases Bulletin, 47 (1950), 907-915.

[18]

National Institute of Allergy and Infectious Diseases Publication No. 02-7139, Malaria, 2002.

[19]

R. Ross, The Prevention of Malaria 1911.

[20]

M. S. Sissoko, Malaria incidence in relation to rice cultivation in the Irrigated sahel of Mali, Acta Tropica, 89 (2004), 161-170. doi: 10.1016/j.actatropica.2003.10.015.

[21]

N. Sogoba, Malaria transmission dynamics in Niono, Mali: The effect of the irrigation systems, Acta Tropica, 101 (2007), 232-240.

[22]

J. TumwiineJ. Y. T. Mugisha and L. S. Luboobi, On oscillatory pattern of malaria dynamics in a population with temporary immunity, Computational and Mathematical Methods in Medicine, 8 (2007), 191-203. doi: 10.1080/17486700701529002.

[23]

A. P. P. WyseL. Bevilacqua and M. Rafikov, Simulating malaria model for different treatment intensities in a variable environment, Ecological Modelling, 206 (2007), 322-330.

show all references

References:
[1]

R. AguasL. J. WhiteR. W. Snow and M. G. M. Gomes, Prospects for malaria eradication in Sub-Saharan Africa, PLoS ONE., 3 (2008), e1767.

[2]

S. AkbariN. K. Vaidya and L. M. Wahl, The time distribution of sulfadoxine-pyrimethamine protection from malaria, Bulletin of Mathematical Biology, 74 (2012), 2733-2751.

[3]

N. Bacaer, Approximation of the basic reproduction number R0 for vector-borne diseases with a periodic vector population, Bulletin of Mathematical Biology, 69 (2007), 1067-1091. doi: 10.1007/s11538-006-9166-9.

[4]

J. -F. Belieres, L. Barret, Z. Charlotte Sama and M. Kuper, https://hal.archives-ouvertes.fr/cirad-00190904/document

[5]

http://www.cdc.gov/malaria/about/disease.html.

[6]

N. ChitnisJ. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of Mathematical Biology, 70 (2008), 1272-1296. doi: 10.1007/s11538-008-9299-0.

[7]

B. DembeleA. Friedman and A. A. Yakubu, Mathematical model for optimal use of sulfadoxine-pyrimethamine as a temporary malaria vaccine, Bulletin of Mathematical Biology, 72 (2010), 914-930. doi: 10.1007/s11538-009-9476-9.

[8]

B. DembeleA. Friedman and A. A. Yakubu, Malaria model with periodic mosquito birth and death rates, Journal of Biological Dynamics, 3 (2009), 430-445. doi: 10.1080/17513750802495816.

[9]

K. Dietz, Mathematical models for malaria in different ecological zones, Biometrics 27 808 17TH ST NW Suite 200, Washington, DC 20006-3910: International Biometric Soc. , 1971.

[10]

K. DietzW. H. Wernsdorfer and I. McGregor, Mathematical models for transmission and control of malaria, Malaria: Principles and Practice of Malariology, 2 (1988), 1091-1133.

[11]

M. A. Diuk-Wasser, Vector abundance and malaria transmission in rice-growing villages in Mali, The American Journal of Tropical Medicine and Hygiene, 72 (2005), 725-731.

[12]

G. Dolo, Malaria transmission in relation to rice cultivation in the irrigated Sahel of Mali, Acta Tropica, 89 (2004), 147-159.

[13]

E. E. Frances, Survivorship and distribution of immature Anopheles gambiae sl (Diptera: Culicidae) in Banambani village, Mali, Journal of Medical Entomology, 41 (2004), 333-339.

[14]

N. J. GovellaF. O. Okumu and G. F. Killeen, Insecticide-treated nets can reduce malaria transmission by mosquitoes which feed outdoors, The American Journal of Tropical Medicine and Hygiene, 82 (2010), 415-419.

[15]

G. F. KilleenA. Seyoum and B. G. J. Knols, Rationalizing Historical successes of malaria control in Africa in terms of mosquito resource availability management, The American Journal of Tropical Medicine and Hygiene, 71 (2004), 87-93.

[16]

F. Lardeux, Host choice and human blood index of Anopheles pseudopunctipennis in a village of the Andean valleys of Bolivia-art. no. 8, Malaria Journal, 6 (2007), NIL1-NIL1.

[17]

G. Macdonald, The analysis of infection rates in diseases in which super infection occurs, Tropical Diseases Bulletin, 47 (1950), 907-915.

[18]

National Institute of Allergy and Infectious Diseases Publication No. 02-7139, Malaria, 2002.

[19]

R. Ross, The Prevention of Malaria 1911.

[20]

M. S. Sissoko, Malaria incidence in relation to rice cultivation in the Irrigated sahel of Mali, Acta Tropica, 89 (2004), 161-170. doi: 10.1016/j.actatropica.2003.10.015.

[21]

N. Sogoba, Malaria transmission dynamics in Niono, Mali: The effect of the irrigation systems, Acta Tropica, 101 (2007), 232-240.

[22]

J. TumwiineJ. Y. T. Mugisha and L. S. Luboobi, On oscillatory pattern of malaria dynamics in a population with temporary immunity, Computational and Mathematical Methods in Medicine, 8 (2007), 191-203. doi: 10.1080/17486700701529002.

[23]

A. P. P. WyseL. Bevilacqua and M. Rafikov, Simulating malaria model for different treatment intensities in a variable environment, Ecological Modelling, 206 (2007), 322-330.

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
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
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
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]
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 0.20 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
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
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 $ $\epsilon_d$ $-0.59$
$\eta_m$ $+0.145$ $\eta_m$ $+0.140$
$\alpha_h$ $-0.5$ $\alpha_h$ $-0.5$
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 $ $\epsilon$ $-0.047$
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 $ $\epsilon$ $-0.047$
[1]

Expeditho Mtisi, Herieth Rwezaura, Jean Michel Tchuenche. A mathematical analysis of malaria and tuberculosis co-dynamics. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 827-864. doi: 10.3934/dcdsb.2009.12.827

[2]

Jaroslaw Smieja, Malgorzata Kardynska, Arkadiusz Jamroz. The meaning of sensitivity functions in signaling pathways analysis. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2697-2707. doi: 10.3934/dcdsb.2014.19.2697

[3]

Kazimierz Malanowski, Helmut Maurer. Sensitivity analysis for state constrained optimal control problems. Discrete & Continuous Dynamical Systems - A, 1998, 4 (2) : 241-272. doi: 10.3934/dcds.1998.4.241

[4]

Zindoga Mukandavire, Abba B. Gumel, Winston Garira, Jean Michel Tchuenche. Mathematical analysis of a model for HIV-malaria co-infection. Mathematical Biosciences & Engineering, 2009, 6 (2) : 333-362. doi: 10.3934/mbe.2009.6.333

[5]

Kazeem Oare Okosun, Robert Smith?. Optimal control analysis of malaria-schistosomiasis co-infection dynamics. Mathematical Biosciences & Engineering, 2017, 14 (2) : 377-405. doi: 10.3934/mbe.2017024

[6]

Yoichi Enatsu, Yukihiko Nakata. Stability and bifurcation analysis of epidemic models with saturated incidence rates: An application to a nonmonotone incidence rate. Mathematical Biosciences & Engineering, 2014, 11 (4) : 785-805. doi: 10.3934/mbe.2014.11.785

[7]

Hui Cao, Yicang Zhou, Zhien Ma. Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1399-1417. doi: 10.3934/mbe.2013.10.1399

[8]

Chengxia Lei, Fujun Li, Jiang Liu. Theoretical analysis on a diffusive SIR epidemic model with nonlinear incidence in a heterogeneous environment. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4499-4517. doi: 10.3934/dcdsb.2018173

[9]

Seung-Yeal Ha, Shi Jin. Local sensitivity analysis for the Cucker-Smale model with random inputs. Kinetic & Related Models, 2018, 11 (4) : 859-889. doi: 10.3934/krm.2018034

[10]

Lorena Bociu, Jean-Paul Zolésio. Sensitivity analysis for a free boundary fluid-elasticity interaction. Evolution Equations & Control Theory, 2013, 2 (1) : 55-79. doi: 10.3934/eect.2013.2.55

[11]

Hamed Azizollahi, Marion Darbas, Mohamadou M. Diallo, Abdellatif El Badia, Stephanie Lohrengel. EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity. Mathematical Biosciences & Engineering, 2018, 15 (4) : 905-932. doi: 10.3934/mbe.2018041

[12]

Qilin Wang, S. J. Li. Higher-order sensitivity analysis in nonconvex vector optimization. Journal of Industrial & Management Optimization, 2010, 6 (2) : 381-392. doi: 10.3934/jimo.2010.6.381

[13]

Alireza Ghaffari Hadigheh, Tamás Terlaky. Generalized support set invariancy sensitivity analysis in linear optimization. Journal of Industrial & Management Optimization, 2006, 2 (1) : 1-18. doi: 10.3934/jimo.2006.2.1

[14]

Krzysztof Fujarewicz, Krzysztof Łakomiec. Parameter estimation of systems with delays via structural sensitivity analysis. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2521-2533. doi: 10.3934/dcdsb.2014.19.2521

[15]

Zhenhua Peng, Zhongping Wan, Weizhi Xiong. Sensitivity analysis in set-valued optimization under strictly minimal efficiency. Evolution Equations & Control Theory, 2017, 6 (3) : 427-436. doi: 10.3934/eect.2017022

[16]

Behrouz Kheirfam, Kamal mirnia. Comments on ''Generalized support set invariancy sensitivity analysis in linear optimization''. Journal of Industrial & Management Optimization, 2008, 4 (3) : 611-616. doi: 10.3934/jimo.2008.4.611

[17]

Behrouz Kheirfam, Kamal mirnia. Multi-parametric sensitivity analysis in piecewise linear fractional programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 343-351. doi: 10.3934/jimo.2008.4.343

[18]

Cruz Vargas-De-León. Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes. Mathematical Biosciences & Engineering, 2012, 9 (1) : 165-174. doi: 10.3934/mbe.2012.9.165

[19]

Yihong Xu, Zhenhua Peng. Higher-order sensitivity analysis in set-valued optimization under Henig efficiency. Journal of Industrial & Management Optimization, 2017, 13 (1) : 313-327. doi: 10.3934/jimo.2016019

[20]

Krzysztof Fujarewicz, Krzysztof Łakomiec. Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1131-1142. doi: 10.3934/mbe.2016034

2017 Impact Factor: 0.972

Metrics

  • PDF downloads (4)
  • HTML views (2)
  • Cited by (0)

Other articles
by authors

[Back to Top]