Brucellosis is an infectious disease caused by bacteria Brucella, and it is difficult to detect since its incubation period could be from about two weeks to one year. The most common sources of ...infection are from farms, raw dairy products, bison, horses, and chickens. Humans can acquire the disease from these animals or animal products contaminated with the bacteria. There are studies about the disease transmission among bison and sometimes from bison to humans. Person-to-person transmission is rare but possible. In this study, we formulate an interact bison–human–environment mathematical model that involves the influence of human transmission, chronic brucellosis, and control strategy on the brucellosis dynamics. We conduct both epidemic and endemic analysis and also represent the threshold dynamics characterized by the basic reproduction number. Numerical simulations are carried out to investigate the stability of the equilibrium points and the reproduction numbers for different optimal settings. An optimal control study is applied to seek a control strategy to maintain the disease outbreaks.
COVID-19 is a severe acute respiratory syndrome caused by the Coronavirus-2 virus (SARS-CoV-2). The virus spreads from one to another through droplets from an infected person, and sometimes these ...droplets can contaminate surfaces that may be another infection pathway. In this study, we developed a COVID-19 model based on data and observations in Thailand. The country has strictly distributed masks, vaccination, and social distancing measures to control the disease. Hence, we have classified the susceptible individuals into two classes: one who follows the measures and another who does not take the control guidelines seriously. We conduct epidemic and endemic analyses and represent the threshold dynamics characterized by the basic reproduction number. We have examined the parameter values used in our model using the mean general interval (GI). From the calculation, the value is 5.5 days which is the optimal value of the COVID-19 model. Besides, we have formulated an optimal control problem to seek guidelines maintaining the spread of COVID-19. Our simulations suggest that high-risk groups with no precaution to prevent the disease (maybe due to lack of budgets or equipment) are crucial to getting vaccinated to reduce the number of infections. The results also indicate that preventive measures are the keys to controlling the disease.
This paper presents a mathematical model for dengue disease to understand its dynamics by using a set of differential equations to describe the effects between human and mosquito populations. In this ...model, the human population is divided into fi ve types of individuals: susceptible vaccination fi rst infectious second infectious and recovered and the mosquitoes population is divided into three types of individuals: larva mosquitoes uninfected female mosquitoes and infected female mosquitoes The epidemic and endemic analysis have also presented along with numerical simulations to verify our model. Our results suggested that the prevention and control of dengue outbreaks can be implemented in an optimal way.
