A Mathematical Model for the Dynamics of Zika Virus via Homotopy Perturbation Method

Abstract

Zika virus is a member of the Flavivirus genus of the Flaviviridae family, which includes other globally relevant human's pathogens such as dengue virus, yellow fever virus, West Nile virus and tick-borne encephalitis virus. In this paper, a deterministic mathematical model of Zika virus was formulated using ordinary differential equations with two control strategies: treatment for humans and insecticide spray for mosquitoes. Homotopy Perturbation Method was used to obtain the approximate solution of the model. From the result obtained, 59% effective administration of insecticide spray proved effective which showed a great reduction in the infected humans as well as infected vector population. Numerical results were offered in the form of Graphs. This research work contributes to new field of knowledge included to the dynamics of Zika virus in population's dynamics with the application of Homotopy Perturbation Method and can be further extended to study the pattern of Zika associated diseases that pose a significant public health risk. © JASEM https://dx.doi.org/10.4314/jasem.v21i4.1

Modelling for the Reduction and Spread Transmission of the Dynamics and Control of Zika virus Disease: Using Ordinary Differential Equations

“…The Model Formulation: In this research work, the instrument use to investigate the model formulated is a deterministic method of ODE using MAPLE 18 software for analysis. Similarly, the model is an extension of Adamu et al,(2017). This model analyse the basic reproduction number, endemic state and global stability in order to reduce the threat in a population and awareness.…”

“…This model analyse the basic reproduction number, endemic state and global stability in order to reduce the threat in a population and awareness. While Adamu et al, (2017) developed a model from an existing model of Ebenezer and Kazeem, (2016) and employed HPM to analyse the error.…”

Analytical Solution of the Effect of Awareness Program by Media on the Spread of an Infectious Disease by Homotopy Perturbation Method

“…G. Devipriya [5], considered a mathematical model of dengue virus transmission consists of human and mosquito compartments by incorporating with control strategy of imperfect treatment and delay in vector maturation whose analytical solution is obtained using HPM. G. Adambu et al [2], considered mathematical model of Zika virus with two control strategies namely treatment for human and insecticide spray for mosquito and used HPM to get approximate solution and shows that 59% effective administration of infectious spray proved a great reduction in the infected human as well as infected vector population.…”

Numerical analysis of the prevention with vaccination against Zika virus (ZIKV)

“…In 2016 three experimental vaccines were created Zika protected monkeys against the virus, an encouraging sign while investigations now pass to studies with people [7]. Some mathematical modeling studies that integrate vaccination are found in [1,2,3].…”