Modeling and optimal control analysis of Zika virus with media impact

Srivastav, Akhil Kumar; Goswami, Naba Kumar; Ghosh, Mini; Li, Xuezhi

doi:10.1007/s40435-018-0416-0

Cited by 13 publications

(10 citation statements)

References 10 publications

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“…The existence of backward bifurcation is explored using the Center Manifold Theory (CMT) made popular by Castillo-Chavez and Song [8] and has been used in the study of some epidemiological models [11,21,26,27,30,38]. For convenience, consider the following change of variables:…”

Section: Existence Of Backward Bifurcationmentioning

confidence: 99%

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Olaniyi

Okosun

Adesanya

et al. 2020

Journal of Biological Dynamics

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A mathematical model of malaria dynamics with naturally acquired transient immunity in the presence of protected travellers is presented. The qualitative analysis carried out on the autonomous model reveals the existence of backward bifurcation, where the locally asymptotically stable malaria-free and malaria-present equilibria coexist as the basic reproduction number crosses unity. The increased fraction of protected travellers is shown to reduce the basic reproduction number significantly. Particularly, optimal control theory is used to analyse the non-autonomous model, which incorporates four control variables. The existence result for the optimal control quadruple, which minimizes malaria infection and costs of implementation, is explicitly proved. Effects of combining at least any three of the control variables on the malaria dynamics are illustrated. Furthermore, the cost-effectiveness analysis is carried out to reveal the most cost-effective strategy that could be implemented to prevent and control the spread of malaria with limited resources.

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Section: Existence Of Backward Bifurcationmentioning

confidence: 99%

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Olaniyi

Okosun

Adesanya

et al. 2020

Journal of Biological Dynamics

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“…The following prevention and control measures were concluded: decreasing contact rate of humans and mosquitoes by using mosquito nets, windows and clothes, increasing the autoimmunity to reduce the transmission rate from mosquitoes to humans, rising the death rate of mosquitoes by using insecticide. As different control parameters were introduced in mathematical models to reduce ZIKV transmission, the impact of media is one of the recently included parameter [95]. The mathematical model formulated by inclusion of impact of media consider SIR-type model for host (human) and SI-type Prasad et al Beni-Suef Univ J Basic Appl Sci (2022) 11:102 model for vector (mosquito) population by involving the possible routes of ZIKV transmission: mosquito borne and sexual transmission.…”

Section: Mathematical Modeling For Zika Virusmentioning

confidence: 99%

Mathematical modeling in perspective of vector-borne viral infections: a review

Prasad

Sagar

Parveen

et al. 2022

Beni-Suef Univ J Basic Appl Sci

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Background Viral diseases are highly widespread infections caused by viruses. These viruses are passing from one human to other humans through a certain medium. The medium might be mosquito, animal, reservoir and food, etc. Here, the population of both human and mosquito vectors are important. Main body of the abstract The main objectives are here to introduce the historical perspective of mathematical modeling, enable the mathematical modeler to understand the basic mathematical theory behind this and present a systematic review on mathematical modeling for four vector-borne viral diseases using the deterministic approach. Furthermore, we also introduced other mathematical techniques to deal with vector-borne diseases. Mathematical models could help forecast the infectious population of humans and vectors during the outbreak. Short conclusion This study will be helpful for mathematical modelers in vector-borne diseases and ready-made material in the review for future advancement in the subject. This study will not only benefit vector-borne conditions but will enable ideas for other illnesses.

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“…The objective functional for fixed time t f . Following the same notation as described in [20,21] we get:…”

Section: The Optimal Control Analysismentioning

confidence: 99%

“…Moreno V M et al [14] presented a multi-patch model to see the effect of the role of short-term dispersal dynamics of ZIKV disease. Srivastav A K et al [21] constructed a new ZIKV model with media impact for the human population and standard mass-action type incidence to reduce the transmission.…”

Section: Introductionmentioning

confidence: 99%

Stability and optimal control analysis of Zika virus with saturated incidence rate

Naba¹,

Shanmukha²

2020

Malaya J. Mat.

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Stability analysis of a non-linear mathematical model is studied and analyzed the transmission dynamics of the Zika virus disease. In our model, the human to human sexual transmission of Zika virus is modeled by considering the saturated incidence rate. This assumption is reasonable as it incorporates the behavioral change of the susceptible individuals and the crowding effect of the infective individuals. The equilibria of the proposed model are obtained and the basic reproduction number (R 0) is computed. The model also exhibits backward bifurcation where the stable disease-free equilibrium coexists with a stable endemic equilibrium, which suggests that the R 0 < 1 is not enough to eradicate the disease. The sensitivity analysis of the parameters of the basic reproduction number of the model is presented. The sensitivity analysis is performed to distinguish the main variables that affect the basic reproduction number, which can be regulated to control the transmission dynamics of the Zika. Finally, the optimal control strategies are incorporated into the model and performed a numerical simulation to support our analytical findings.

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Modeling and optimal control analysis of Zika virus with media impact

Cited by 13 publications

References 10 publications

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Mathematical modeling in perspective of vector-borne viral infections: a review

Stability and optimal control analysis of Zika virus with saturated incidence rate

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