Dynamics and optimal control of a stochastic Zika virus model with spatial diffusion

Area of Science:

• Epidemiology
• Mathematical Biology
• Public Health

Background:

• Zika virus poses a global health threat due to its severe congenital disabilities, particularly microcephaly.
• Multiple transmission routes, including vector-borne, sexual, and vertical, complicate disease control efforts.

Purpose of the Study:

• To develop and analyze a stochastic reaction-diffusion model (SRDM) for Zika virus transmission.
• To investigate conditions for Zika virus extinction and the existence of a stable disease state.
• To formulate an optimal control strategy for mitigating Zika virus spread.

Main Methods:

• Establishment of a stochastic reaction-diffusion model incorporating human-mosquito, human-human sexual, and mosquito vertical transmission.
• Mathematical analysis to prove the existence, uniqueness, and boundedness of the model's solutions.
• Formulation of an optimal control problem with interventions like personal protection, treatment, and insecticide application.

Main Results:

• Sufficient conditions for the extinction of Zika virus were determined.
• The existence of a stationary distribution for positive solutions was established.
• Numerical simulations demonstrated the effectiveness of integrated control strategies.

Conclusions:

• The developed SRDM provides a robust framework for understanding Zika virus dynamics.
• Optimal control strategies can effectively reduce Zika virus prevalence and associated costs.
• Integrated public health interventions are crucial for managing infectious diseases like Zika.