Waterborne diseases are present major health problems to humanity especially in rural communities where many individuals belong to the lower socioeconomic classes (SECs). The impacts of introducing waterborne disease control measures for such communities are investigated by considering a waterborne disease model. The model is extended by introducing treatment of infected individuals and water purification as control measures. The possible benefits of considering these control measures for the various SECs are investigated. Further analyses show how different degrees of control impact the rate at which waterborne diseases are spread across SECs. The disease control model is validated by using it to study the cholera outbreak in Haiti.
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References
1.
BertuzzoE., MariL., RighettoL., et al.2011. Prediction of the spatial evolution and effects of control measures for the unfolding Haiti cholera outbreak. Geophys. Res. Lett. 38, L06403.
2.
CapassoV., and Paveri-FontanaS.L.1979. A mathematical model for the 1973 cholera epidemic in the European Mediterranean region. Rev. Epidemol. Sante. 27, 121–132.
ChaoD.L., HalloranM.E., and LonginiI.M.2011. Vaccination strategies for epidemic cholera in Haiti with implications for the developing world. Proc. Natl. Acad. Sci. USA. 108, 7081–7085.
6.
ChunaraR., AndrewsJ.R., and BrownsteinJ.S.2012. Social and news media enable estimation of epidemiological patterns early in the 2010 Haitian cholera outbreak. Am. J. Trop. Med. Hyg. 86, 39–45.
7.
CodecoC.T.2001. Endemic and epidemic of cholera: The role of the aquatic reservoir. BMC Infect. Dis. 1, 1.
8.
CollinsO.C., and DuffyK.J.2016. Optimal control intervention strategies using an n-patch waterborne disease model. Nat. Resour. Model. 29, 499–519.
9.
CollinsO.C., and GovinderK.S.2014. Incorporating heterogeneity into the transmission dynamics of a waterborne disease model. J. Theor. Biol. 356, 133–143.
10.
CollinsO.C., and GovinderK.S.2016. Stability analysis and optimal vaccination of a waterborne disease model with multiple water sources. Nat. Resour. Model. 29, 426–447.
11.
CollinsO.C., RobertsonS.L., and GovinderK.S.2015. Analysis of a waterborne disease model with socioeconomic classes. Math. Biosci. 269, 86–93.
12.
EisenbergM.C., RobertsonS.L., and TienJ.H.2013. Identifiability and estimation of multiple transmission pathways in cholera and water borne disease. J. Theor. Biol. 324, 84–102.
13.
GhoshM., ChandraP., SinhaP., and ShuklaJ.B.2004. Modeling the spread of carrier-dependent infectious diseases with environmental effect. Appl. Math. Comput. 154, 385–402.
14.
HartleyD.M., MorrisJ.G., and SmithD.L.2006. Hyperinfectivity: A critical element in the ability of V. cholerae to cause epidemics?. PLoS Med. 3, 63–69.
15.
HeesterbeekJ.A.P., and RobertsM.G.2007. The type-reproduction number in models for infectious disease control. Math. Biosci. 206, 3–10.
16.
Hove-MusekwaS.D., NyabadzaF., ChiyakaC., et al. (2011). Modelling and analysis of the effects of malnutrition in the spread of cholera. Math. Comput. Modell. 53, 1583–1595.
17.
KaraT.K., and BatabyalA.2011. Stability analysis and optimal control of an SIR epidemic model with vaccination. BioSystems, 104, 127–135.
18.
KingA.A., LonidesE.L., PascualM., and BoumaM.J.2008. Inapparent infections and cholera dynamics. Nature, 454, 877–881.
19.
LucasM.E., DeenJL, von SeidleinL, et al.2005. Effectiveness of mass oral cholera vaccination in Beira, Mozambique. N. Engl. J. Med. 352, 757–767.
20.
Miller NeilanR.L., SchaeferE., GaffH., et al.2010. Modelling optimal intervention strategies for cholera. Bull. Math Biol. 72, 2004–2018.
21.
MSPP Haiti (Ministry of Public Health and Population Haiti). 2013. Available at: http://mspp.gouv.ht/newsite.
22.
MukandavireZ., LiaoS., WangJ., et al. (2011a). Estimating the reproduction numbers for the 2008–2009 cholera outbreak in Zimbabwe. Proc. Natl. Acad. Sci. USA. 108, 8767–8772.
23.
MukandavireZ., SmithD.L., and MorrisJ.G. Jr. 2013. Cholera in Haiti: Reproductive numbers and vaccination coverage estimates. Sci. Rep. 3, 997.
24.
MukandavireZ., TripathiA., ChiyakaC., et al. (2011b). Modelling and analysis of the intrinsic dynamics of cholera. Differ. Equ. Dyn. Syst. 19, 253–265.
25.
MwasaA., and TchuencheJ.M.2011. Mathematical analysis of a cholera model with public health interventions. BioSystems, 105, 190–200.
26.
PourabbasE., d'OnofrioA., and RafanelliM.2001. A method to estimate the incidence of communicable diseases under seasonal fluctuations with application to cholera. Appl. Math. Comput. 118, 161–174.
27.
RobertsM.G., and HeesterbeekJ.A.P.2003. A new method for estimating the effort required to control an infectious disease. Proc. R. Soc. Lond. B, 270, 1359–1364.
28.
RobertsonS.L., EisenbergM.C., and TienJ.H.2013. Heterogeneity in multiple transmission pathways: Modelling the spread of cholera and other waterborne disease in networks with a common water source. J. Biol. Dynam. 7, 254–275.
29.
RootE.D., RoddJ., YunusM., and EmchM.2013. The Role of Socioeconomic Status in longitudinal trends of cholera in Matlab, Bangladesh, 1993–2007. PLoS Negl. Trop. Dis. 7, e1997.
30.
SanchesR.P., FerreiraP.F., and KraenkelR.A.2011. The role of immunity and seasonality in cholera epidemics. Bull. Math. Biol. 73, 2916–2931.
31.
TchuencheJ.M., KhamisS.A., AgustoF.B., and MpesheS.C.2011. Optimal control and sensitivity analysis of an influenza model with treatment and vaccination. Acta Biotheor. 59, 1–28.
32.
Matlab. 2012b. The MathWorks, Inc., Version 08:37:39, R2012b.
33.
TienJ.H., and EarnD.J.D.2010. Multiple transmission pathways and disease dynamics in a waterborne pathogen model. Bull. Math. Biol. 72, 1506–1533.
34.
TuiteA.R., TienJ., EisenbergM., et al.2011. Cholera epidemic in Haiti, 2010: Using a transmission model to explain spatial spread of disease and identify optimal control interventions. Ann. Intern. Med. 154, 593–601.
35.
UNICEF. 2012. Child Mortality Report (Prepared at UNICEF Headquarters by Danzhen You, Jin Rou new, and Tessa Wardlaw on behalf of the United Nations Inter-agency Group for Child Mortality Estimation.)
36.
van den DriesscheP., and WatmoughJ.2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48.
