Fractional insights into Zika virus transmission: Exploring preventive measures from a dynamical perspective

Abstract

Mathematical models for infectious diseases can help researchers, public health officials, and policymakers to predict the course of an outbreak. We formulate an epidemic model for the transmission dynamics of Zika infection with carriers to understand the intricate progression route of the infection. In our study, we focused on the visualization of the transmission patterns of the Zika with asymptomatic carriers, using fractional calculus. For the validity of the model, we have shown that the solutions of the system are positive and bounded. Moreover, we conduct a qualitative analysis and examine the dynamical behavior of Zika dynamics. The existence and uniqueness of the solution of the system have been proved through analytic skills. We establish the necessary conditions to ensure the stability of the recommended system based on the Ulam–Hyers stability concept (UHS). Our research emphasizes the most critical factors, specifically the mosquito biting rate and the existence of asymptomatic carriers, in increasing the complexity of virus control efforts. Furthermore, we predict that the asymptomatic fraction has the ability to spread the infection to non-infected regions. Furthermore, treatment due to medication, the fractional parameter or memory index, and vaccination can serve as effective control measures in combating this viral infection.

Keywords

• fractional calculus
• zika virus infection
• mathematical model
• vaccination and treatment
• stability analysis
• dynamical behavior