This study discusses the sensitivity analysis of parameters, namely the COVID-19 model, by dividing the population into seven subpopulations: susceptible, exposed, symptomatic infection, asymptomatic infection, quarantine, isolation, and recovered. The solution to the ordinary differential equation for the COVID-19 model using the fourth-order Runge-Kutta numerical method explains that COVID-19 is endemic, as evidenced by the basic reproduction number (𝑅 0 ) of 7.5. It means 1 individual can infect 7 to 8 individuals. Then 𝑅 0 is calculated using the next-generation matrix method. Based on the value of 𝑅 0 , a parameter sensitivity analysis is implemented to specify the most influential parameters in the spread of the COVID-19 outbreak. This can provide input on the selection of appropriate control measures to solve the epidemic from COVID-19. The results of the sensitivity analysis are the parameters that have the most influence on the model, namely Λ, 𝑞

No abstract

Cholera is an acute diarrheal disease that spread quickly in an unsanitary environment, and one of its control measures is employing quarantine. Therefore, this research aims to construct a model for the spread of SIRQB-type (susceptibles, infective, recovered, quarantine, bacteria) infectious diseases through a nonlinear differential equation approach. Furthermore, the equilibrium points condition and their stability were investigated using the standard dynamical analysis method. The results show two points of equilibrium: the disease-free, which always exists and is unstable, and the endemic, which is stable and exists under certain conditions. Also, the simulation carried out support the analysis results, and it shows that the rate of quarantine affects the spread of the infected subpopulation.

Comorbidity is defined as the coexistence of two or more diseases in a person at the same time. The mathematical analysis of the COVID-19 model with comorbidities presented includes model validation of cumulative cases infected with COVID-19 from 1 November 2020 to 19 May 2021 in Indonesia, followed by positivity and boundedness solutions, equilibrium point, basic reproduction number (R0), and stability of the equilibrium point. A sensitivity analysis was carried out to determine how the parameters affect the spread. Disease-free equilibrium points are asymptotically stable locally and globally if R0 < 1 and endemic equilibrium points exist, locally and globally asymptotically stable if R0 > 1. In addition, this disease is endemic in Indonesia, with R0 = 1.47. Furthermore, two optimal controls, namely public education and increased medical care, are included in the model to determine the best strategy to reduce the spread of the disease. Overall, the two control measures were equally effective in suppressing the spread of the disease as the number of COVID-19 infections was significantly reduced. Thus, it was concluded that more attention should be paid to patients with COVID-19 with underlying comorbid conditions because the probability of being infected with COVID-19 is higher and mortality in this population is much higher. Finally, the combined control strategy is an optimal strategy that provides an effective guarantee to protect the public from the COVID-19 infection based on numerical simulations and cost evaluations.

We applied sensitivity analysis and optimum control to the COVID-19 model in this research. In addition, the basic reproduction number calculated as 1.57 indicates that this illness is widespread across Indonesia. The most important factor in this model is the contact rate with infected people, with or without comorbidity. Optimal control will minimize the number of infected populations without and with comorbidity, and costs. Numerical experiments will be carried out to describe and compare the graphical models of the spread of COVID-19 with and without controls. From the numerical results and cost-effectiveness analysis on the optimal control problem, it is found that applying a combination of controls can give the best results compared to a single control