SEIHR-SEI Mathematical Model of Zika Virus Transmission with Vector Control - Shiddiqie, Ichwal Afrizan; Khumaeroh, Mia Siti; Zulkarnaen, Diny; Diana, Arista Fitri (Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung, 2024)
Zika virus (ZIKV) is transmitted by Aedes Aegypti mosquito, which is recognized as a vector for viruses causing dengue fever and chikungunya. This study uses SEIHR‐SEI mathematical model to analyze the dynamics of Zika virus transmission. In this model, human population (host) is classified into five compartments: Susceptible Humans (Sh), Exposed Humans (Eh), Infected Humans (Ih), Hospitalized Humans (Hh) and Recovered Humans (Rh). Meanwhile, the mosquito population (vector) is divide into three compartments: Susceptible Vectors (Sv), Exposed Vectors (Ev), and Infected Vectors (Iv). Stability analysis is conducted using Routh‐Hurwitz criteria for assessing local stability and Lyapunov function for evaluating global stability. Moreover, Basic Reproduction Number (R0), which represents the average number of new infections produced by one infected individual in a susceptible population, is derived by using the Next Generation Matrix (NGM) method. The result shows that the equilibrium point for disease‐free conditions is globally asymptotic stable when R0 < 1, meanwhile the equilibrium point for endemic conditions is stable when R0 > 1. The simulation result using endemic data and sensitivity analysis of three parameters, including contact rate between susceptible humans and infected humans (c), hospitalization rate of infected individuals (τ ), and mosquito control rate (ω), reveals that c and ω exert a more significant effect on changes in R0 compared to τ . Therefore, minimizing contact with infected individuals or implementing vector control is more effective than isolating or hospitalizing infected patients.