Bifurcation and Sensitivity Analysis of Malaria–Schistosomiasis Co-infection Model

Bakare, Emmanuel A.; Nwozo, Chuma Raphael

doi:10.1007/s40819-017-0394-5

Cited by 19 publications

(11 citation statements)

References 31 publications

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“…In addition, several authors have formulated mathematical models describing the dynamics of coinfectious diseases. The works of Okosun and Makinde (2014), Bakare and Nwozo (2017), Mensah et al (2018), Hanif (2018), Gumel et al (2009), Mutua and Vaidya (2015), and Fatmawati and Tasman (2016) on coinfection dynamics have proved very effective in mathematical model formulation and in the analysis performed in this study. Furthermore, the basic reproduction number is an important epidemic threshold used in determining the average number of secondary infections when an infected individual is introduced into an entirely susceptible host population (Anderson and May, 1999;Diekmann et al, 2010;Hethcote, 1994;Van den Driessche and Watmough, 2002).…”

Section: Introductionmentioning

confidence: 83%

“…Definition 1. The normalized forward sensitivity index of a variable h with respect to parameter z q is given by ξ = ∂h ∂zq × zq h (see Bakare and Nwozo, 2017).…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…Definition 2. The sensitivity and elasticity of the basic reproduction number R omt with respect to β o are given by ξ Romt βo = ∂Romt ∂βo × βo Romt (see Bakare and Nwozo, 2017) The positive signs of the sensitivity indices of the parameters of the basic reproduction number show that increases in the values of all of the parameters lead to an increase in the reproduction number of the disease. The forces of infection parameters β o , β k positively increase the reproduction number.…”

Section: Sensitivity Analysismentioning

confidence: 99%

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Mathematical Modeling of the Coinfection Dynamics of Malaria-Toxoplasmosis in the Tropics

Ogunmiloro

2019

Biometrical Letters

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Coinfection by Plasmodium species and Toxoplasma gondii in humans is widespread, with its endemic impact mostly felt in the tropics. A mathematical model is formulated as a first-order nonlinear system of ordinary differential equations to describe the coinfection dynamics of malariatoxoplasmosis in the mainly human and feline susceptible host population in tropical regions. Comprehensive mathematical techniques are applied to show that the model system is bounded, positive and realistic in an epidemiological sense. Also, the basic reproduction number (R omt ) of the coinfection model is obtained. It is shown that if R omt < 1, the model system at its malaria-toxoplasmosis absent equilibrium is both locally and globally asymptotically stable. The impact of toxoplasmosis and its treatment on malaria, and vice versa, is studied and analyzed. Sensitivity analysis was performed to investigate the impact of the model system parameters on the reproduction number of the transmission of malaria-toxoplasmosis coinfection. Simulations and graphical illustrations were made to validate the results obtained from the theoretical model.

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Section: Introductionmentioning

confidence: 83%

“…Definition 1. The normalized forward sensitivity index of a variable h with respect to parameter z q is given by ξ = ∂h ∂zq × zq h (see Bakare and Nwozo, 2017).…”

Section: Sensitivity Analysismentioning

confidence: 99%

Section: Sensitivity Analysismentioning

confidence: 99%

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Mathematical Modeling of the Coinfection Dynamics of Malaria-Toxoplasmosis in the Tropics

Ogunmiloro

2019

Biometrical Letters

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“…A coinfection is the infection of a host with two or more different pathogens or different strains of the same pathogens, leading to coexistence of strains (pathogens) at population level [14]. Mathematical modeling of infectious diseases such as coinfection of HIV/AIDS and opportunistic infection is regarded as a fundamental tool in understanding the dynamics and helpful in the decision-making processes regarding intervention strategies and measures required for disease elimination and/or control [15,16].…”

Section: Introductionmentioning

confidence: 99%

HIV/AIDS-Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation

Teklu

Mekonnen

2021

Journal of Applied Mathematics

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In the paper, we have considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia coinfection in a human population at different infection stages. Our model revealed that the disease-free equilibrium points of the HIV/AIDS and pneumonia submodels are both locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R H and R P ) are less than unity. Both the submodel endemic equilibrium points are locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R P and R H ) are greater than unity. The full HIV/AIDS-pneumonia coinfection model has both locally and globally asymptotically stable disease-free equilibrium points whenever the basic reproduction number of the coinfection model R H P is less than unity. Using standard values of parameters collected from different kinds of literature, we found that the numerical values of the basic reproduction numbers of the HIV/AIDS-only submodel and pneumonia-only submodel are 17 and 7, respectively, and the basic reproduction number of the HIV/AIDS-pneumonia coinfection model is max 7 , 17 = 17 . Applying sensitive analysis, we identified the most influential parameters to change the behavior of the solution of the considered coinfection dynamical system are the HIV/AIDS and pneumonia transmission rates β 1 and β 2 , respectively. The coinfection model was numerically simulated to investigate the stability of the coinfection endemic equilibrium point, the impacts of transmission rates, and treatment strategies for HIV/AIDS-only, pneumonia-only, and HIV/AIDS-pneumonia coinfected individuals. Finally, we observed that numerical simulations indicate that treatment against infection at every stage lowers the rate of infection or disease prevalence.

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“…Elmojtaba (2016) formulated a mathematical model to study the co-infection dynamics of malaria and visceral leishmaniasis. Bakare and Nwozo (2016) Co-infection Model Formulation to Evaluate the Transmission…..…”

mentioning

confidence: 99%

Co-infection Model Formulation to Evaluate the Transmission Dynamics of Malaria and Dengue Fever Virus

Oluwafemi¹,

Akinwande²,

Olayiwola³

et al. 2020

jasem

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A mathematical model of the co-infection dynamics of malaria and dengue fever condition is formulated. In this work, the Basic reduction number is computed using the next generation method. The diseasefree equilibrium (DFE) point of the model is obtained. The local and global stability of the disease-free equilibrium point of the model is established. The result show that the DFE is locally asymptotically stable if the basic reproduction number is less than one but may not be globally asymptotically stable. Keywords: Malaria; Dengue Fever; Co-infection; Basic reproduction number; Disease-Free equilibrium

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Bifurcation and Sensitivity Analysis of Malaria–Schistosomiasis Co-infection Model

Cited by 19 publications

References 31 publications

Mathematical Modeling of the Coinfection Dynamics of Malaria-Toxoplasmosis in the Tropics

Mathematical Modeling of the Coinfection Dynamics of Malaria-Toxoplasmosis in the Tropics

HIV/AIDS-Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation

Co-infection Model Formulation to Evaluate the Transmission Dynamics of Malaria and Dengue Fever Virus

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