A mathematical model of Zika virus transmission with saturated incidence and optimal control: A case study of 2016 zika outbreak in Puerto Rico

ABSTRACT

Zika virus outbreak is creating a global public health hazard due to its increasing prevalence rate and neurological complication in affected individuals. In this work we have developed and studied an ODE compartmental Zika model with non-linear saturated incidence function and three control measures including prevention control from vector bite, treatment control of infected host and vector killing control. Our theoretical analysis shows that the disease free equilibrium is locally as well as globally asymptotically stable when the basic reproduction number is less than unity. The virus is uniformly persistent when the basic reproduction number is greater than unity. An endemic equilibrium point exists and locally stable when the basic reproduction number is greater than unity. The model is validated by fitting the model to real reported data of 2016 Zika outbreak in Puerto Rico and estimated the model parameters. We also have studied the basic reproduction number and effective reproduction number of the outbreak. Sensitivity analysis has been carried out to find most sensitive parameters. The optimal control and efficiency analysis has been done to find the policy of control variables. Lastly, the manuscript is ended by some conclusions.

KEYWORDS:

• Zika virus
• basic reproduction number
• stability analysis
• data fitting
• parameter estimation
• sensitivity analysis
• optimal control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Sudhanshu Kumar Biswas

Sudhanshu Kumar Biswas is an Assistant Professor of Mathematics in Sripat Singh College, West Bengal, India, and a research scholar of Department of Applied Mathematics, University of Calcutta. He is working on the mathematical modelling on infectious diseases. He has 6 publications in a reputed international journal.

Uttam Ghosh

Uttam Ghosh is an Assistant Professor of Applied Mathematics in University of Calcutta. His research includes Biomathematics and Fractional calculus. He has more than 90 publications in reputed national and international journals.

Susmita Sarkar

Susmita Sarkar is a Professor of Applied Mathematics at the University of Calcutta. Her field of research includes plasma dynamics, biomathematics, and fractional calculus. She has more than 100 research publications in reputed international journals. She was regular associate of ICTP and also associate of TWAS.