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On the approximate solutions and asymptotic stability of an onchocerciasis transmission model

International Journal of Modeling, Simulation, and Scientific Computing 2021年第5期12卷 193-209页

作者： oluwatayo michael ogunmiloro Department of Mathematics Ekiti State University Ado EkitiEkiti StateNigeria

This article describes the mathematical model derivation describing river blindness disease transmission in human and vector(blackflies)host *** effect of incomplete resistance to re-infection in human individuals who recovered from the disease after treatment but are still subjected to repeated exposures to infected blackflies bite is ***,the basic reproduction number(Rhb)is obtained and it is shown that if Rhb1,the onchocerciasis-endemic equilibrium is globally asymptotically ***,the Differential Transform Method(DTM)and Runge–Kutta fourth-order method is employed via the computational software Maple 18 to solve and obtain the approximate solutions of the model system equations,which showed that the numerical results favorably compare with each *** reveal that increase in biting and transmission rates leads to an increase of Rhb and incomplete resistance to re-infection due to consistent exposure to blackflies ***,simulations of the approximate solutions of the model state equations are provided.

关键词： River blindness stability analysis reproduction number numerical methods

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Transmission dynamics of onchocerciasis with two classes of infection and saturated treatment function

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International Journal of Modeling, Simulation, and Scientific Computing 2020年第5期11卷 184-207页

作者： Amos Sesan Idowu oluwatayo michael ogunmiloro Department of Mathematics Faculty of Physical Science University of IlorinIlorinKwara StateNigeria Department of MathematicsFaculty of Science Ekiti State UniversityAdo-EkitiEkiti StateNigeria Oluwatayo Michael

A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is *** this model,the onchocerciasis infected human individuals are divided into two classes of infected humans with high and low microfilarial output incorporating saturated treatment function,which caters for high saturation of onchocerciasis *** analyze the model feasible region and obtain the basic reproduction number(R_(hb))using the next generation matrix ***,we obtain the onchocerciasis-free and onchocerciasis endemic equilibrium solutions and show that if R_(hb) is less than unity,the onchocerciasis-free equilibrium is locally and globally asymptotically ***,we employed a Lyapunov function to analyze the global asymptotic stability of the onchocerciasis—endemic equilibrium whenever Rhb is greater than *** addition,data on mass drug distribution of ivermectin drug to combat onchocerciasis prevalence in Ekiti state of Nigeria were fitted to the *** results reveal that consistent annual or bi-annual distribution of ivermectin drug in the region is effective in reducing the disease *** simulations also show that public health control measures are needed to minimize infectious contact between humans and blackflies which leads to onchocerciasis infections and visual blindness.

关键词： Onchocerciasis saturated treatment function basic reproduction number stability analysis

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