A Zika Virus Model Incorporating the Role of Information: Stability, Numerical Methods, and Control Strategies

In this current study, we formulate a new Zika virus model in light of information-induced behavioural change. Firstly, we investigate the model without control and basic mathematical results are obtained. Non-negativity, boundedness, basic reproduction number, sensitivity analysis, and the stability of different equilibrium quantities are discussed. It is observed that disease-free equilibrium (DFE) point is globally asymptotically stable (GAS) if the aware individuals do not participate in the disease progression. Secondly, a nonstandard finite difference (NSFD) scheme is developed for the proposed model. It is observed that, unlike traditional numerical methods such as the Euler and fourth-order Runge-Kutta (RK4) methods, which can fail with larger step sizes, our proposed NSFD method consistently preserves the equilibrium quantities and their stability characteristics. Thereafter, we introduce time dependent controls into the model in order to investigate the optimal effects of information-induced behavioural change, use of condoms, use of insecticide-treated nets, treatment, and indoor residual spraying. Using Pontryagin's Maximum Principle (PMP), the proposed control system is examined and the optimal control profiles for the implemented controls are acquired. Afterward, different combinations of control strategies are applied and compared numerically. It is found that though each combination has its usefulness, the combined effect of all control measures is observed to be highly effective in reducing the spread of the disease and the overall cost.