Zika virus is mosquito-borne flavivirus. It can be transmitted between human by bitting of Aedes mosquitoes. It can also transmit chikungunya, yellow fever and dengue disease. Zika virus can spread through mosquito to human, human to mosquito and human to human. In this paper, we account the age structure of zika virus patiens. We divide into two groups: human and mosquito. Age structure of human population is separated two groups: juvenile and adult human. Standard dynamical modeling method is used for analyzing the behaviors of solutions. The stability conditions for the disease free and endemic equilibrium states are considered by Routh-Hurwitz criteria. We simulate our model by using numerical method. The numerical simulations are showed to confirm the analytical results.

COVID-19 is the name of the new infectious disease which has reached the pandemic stage and is named after the coronavirus (COVs) which causes it. COV is a single-stranded RNA virus which in humans leads to respiratory tract symptoms which can lead to death in those with low immunities, particularly older people. In this study, a standard dynamic model for COVID-19 was proposed by comparing a simple model and the optimal control model to reduce the number of infected people and become a guideline to control the outbreak. Control strategies are the vaccination rate and vaccine-induced immunity. An analysis was performed to find an equilibrium point, the basic reproduction number , and conditions that generate stability by using Lyapunov functions to prove the stability of the solution at the equilibrium point. Pontryagin’s maximum principle was used to find the optimal control condition. Moreover, sensitivity analysis of the parameters was performed to learn about the parameters that might affect the outbreak in order to be able to control the outbreak. According to the analysis, it is seen that the efficacy of vaccines and the infection rate will affect the increased (decreased) incidence of the outbreak. Numerical analyses were performed on the Omicron variant outbreak data collected from the Thailand Ministry of Health, whose analyses then indicated that the optimal control strategy could lead to planning management and policy setting to control the COVID-19 outbreak.

A mathematical model of Zika virus is studied in this paper. Zika is caused by Zika virus, a flavivirus related to yellow fever, dengue. In 1952, first outbreak occurred in Uganda. In 1962, an epidemic was recognized as the first time in Thailand. In this study, we consider the transmission cycle between two population groups: human and mosquito. Using standard dynamical modeling method, the stability conditions of our model is considered by Routh-Hurwitz criteria. The numerical simulations are shown to support the analytical results.

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