The Dynamics of Multiple Species and Strains of Malaria

Agyingi, Ephraim; Ngwa, Matthias; Wiandt, Tamas

doi:10.30707/lib3.1agyingi

Cited by 6 publications

(12 citation statements)

References 7 publications

(8 reference statements)

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“…Maintaining all the assumptions made in the model by Agyingi et al (2016), we add delay parameters to both host and vectors and obtain the governing equations of the model for two species as follows:…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The introduction of an infected human will lead to the infection of α k cases in mosquitos, each of which will lead to σ k cases in humans. R k 0 is computed as the product of the quantities α k and δ k (see Agyingi et al, 2016), that is,…”

Section: Mathematical Modelmentioning

confidence: 99%

“…In addition to the DFE, system (4) has two more equilibrium points as stated in the result below (Agyingi et al, 2016). Lemma 1: If R k 0 > 1 for k = 1, 2, then system (4) possesses two non-DFEs given by…”

Section: Stability Analysismentioning

confidence: 99%

“…Recently, Agyingi, Ngwa, and Wiandt (2016) proposed a model for studying the dynamics of multiple species and strains of malaria. The susceptible-infectious (SI) model for the n species/strains was developed using 2(n+1) ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…While this can be remedied by simply including latent compartments, the resulting system suffers from the downfall of containing many parameters which cannot be determined experimentally. In this paper we upgrade the SI model in Agyingi et al (2016) to incorporate time lags which serve as the incubation periods, for two species of the parasite. We remark here that the derived model can also be used to study two strains of a single species.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stability and Hopf Bifurcation of a Two Species Malaria Model with Time Delays

Agyingi

Wiandt

Ngwa

2017

LiB

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We present a mathematical model of the transmission dynamics of two species of malaria with time lags. The model is equally applicable to two strains of a malaria species. The reproduction numbers of the two species are obtained and used as threshold parameters to study the stability and bifurcations of the equilibria of the model. We find that the model has a disease free equilibrium, which is a global attractor when the reproduction number of each species is less than one. Further, we observe that the non-disease free equilibrium of the model contains stability switches and Hopf bifurcations take place when the delays exceed the critical values.

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

Section: Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability and Hopf Bifurcation of a Two Species Malaria Model with Time Delays

Agyingi

Wiandt

Ngwa

2017

LiB

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Geospatial analysis of malaria mortality in the kintampo health and demographic surveillance area of central Ghana

et al. 2020

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Malaria remains a menace to the existence of humanity in most contexts. Geospatial analysis of malaria mortality is crucial to identifying clusters of high disease burden and areas with limited access to malaria care for targeted control and remedial interventions. This study identified spatial and space-time clusters of malaria mortality in the Kintampo area of central Ghana. We used 1301 malaria deaths archived from 2005 to 2017 and Global Positioning System (GPS) point locations of the sub-districts in which these deaths occurred for our analysis. Mortality risks were smoothed and mapped using the Spatial Empirical Bayesian smoothing technique in Geoda (version 1.12.1.161) whereas spatial and spatio-temporal clustering analysis was done using SaTScan (version 9.6). Malaria mortality risks ranged between 1.2 and 2.4 deaths per 1000 population for persons of all ages and between 3.3 and 6.0 deaths per 1000 population for children under five years of age by sub-district. Two spatial clusters were detected for all-age malaria mortality with only the primary cluster (RR = 1.42, p = 0.001) being statistically significant. Also, two statistically significant space-time clusters were detected for all-age malaria mortality in the study area. The most likely cluster occurred between 2006 and 2011 in five sub-districts with a relative risk of 2.12 (p < 0.001) whilst the secondary cluster which had a relative risk of 2.47 (p < 0.001) occurred between 2005 and 2010 in four sub-districts. Similarly, only the most likely spatial cluster of under-five malaria mortality was statistically significant (RR = 1.36, p = 0.024). Furthermore, three spatio-temporal clusters of under-five malaria mortality were detected in the study area. The primary and second secondary clusters were statistically significant whilst the first secondary cluster had borderline significance. The primary cluster (RR = 4.49, p = 0.002) occurred in two sub-districts between 2006 and 2007. The first secondary cluster (RR = 2.21, P = 0.005) covered four sub-districts and was detected between 2006 and 2011 whereas the second secondary cluster (RR = 2.51, p = 0.003) covered two sub-districts between 2008 and 2013. Ultimately, our analysis identified a number of substantial spatial and apace-time clusters of malaria mortality in the study context, which could aid in the strategic planning, implementation and monitoring of targeted malaria control interventions.

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Modelling of Malaria Transmission Using Delay Differential Equation

Mibei¹,

Wesley²,

Daniel³

2020

MMA

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Malaria is one of the major causes of deaths and ill health in endemic regions of sub-Saharan Africa and beyond despite efforts made to prevent and control its spread. Epidemiological models on how malaria is spread have made a substantial contribution on the understanding of disease changing aspects. Previous researchers have used Susceptible -Exposed-Infectious-Recovered (SEIR) model to explain how malaria is spread using ordinary differential equations. In this paper we develop mathematical SEIR model to define the dynamics of the spread of malaria using Delay differential equations with four control measures such as long lasting treated insecticides bed nets, intermittent preventive treatment of malaria in pregnant women (IPTP), intermittent preventive treatment of malaria in infancy (IPTI) and indoor residual spraying. The model is analyzed and reproduction number derived using next generation matrix method and its stability is checked by Jacobean matrix. Positivity of solutions and boundedness of the model is proved. We show that the disease free equilibrium is locally asymptotically stable if R 0 <1 (R 0 -reproduction number) and is unstable if R 0 >1. Numerical simulation shows that, with proper treatment and control measures put in place the disease is controlled.

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The Dynamics of Multiple Species and Strains of Malaria

Cited by 6 publications

References 7 publications

Stability and Hopf Bifurcation of a Two Species Malaria Model with Time Delays

Stability and Hopf Bifurcation of a Two Species Malaria Model with Time Delays

Geospatial analysis of malaria mortality in the kintampo health and demographic surveillance area of central Ghana

Modelling of Malaria Transmission Using Delay Differential Equation

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