Optimal COVID-19 epidemic strategy with vaccination control and infection prevention measures in Thailand.

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.

Analysing transmission dynamics of HIV/AIDS with optimal control strategy and its controlled state.

HIV is a virus that weakens a person's immune system. HIV has three stages, and AIDS is the most severe stage of HIV (Stage 3). People with HIV should take medicine (called ART) recommended by WHO as soon as possible to reduce the amount of virus in the body. In this paper, we formulate a mathematical model for HIV/AIDS with a new approach by focusing on two groups of infectious individuals, HIV and AIDS. We also introduce a controlled class (treated patients and being monitored), and people in this class can spread the disease. We further investigate the essential dynamics of the model through an equilibrium analysis. Optimal control theory is applied to explore effective treatment strategies by combining two control measures: standard antiretroviral therapy and AIDS treatments. Numerical simulation results show the effects of the two time-dependent controls, and they can be used as guidelines for public health interventions.

On the dynamics of brucellosis infection in bison population with vertical transmission and culling.

We introduce a new mathematical modeling framework that seek to improve our quantitative understanding of the influence of chronic brucellosis and culling control on brucellosis dynamics in periodic and non-periodic environments. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction numbers. In addition, we also perform an optimal control study to explore optimal culling strategy in periodic and non-periodic environment.

Analyzing transmission dynamics of cholera with public health interventions.

Cholera continues to be a serious public health concern in developing countries and the global increase in the number of reported outbreaks suggests that activities to control the diseases and surveillance programs to identify or predict the occurrence of the next outbreaks are not adequate. These outbreaks have increased in frequency, severity, duration and endemicity in recent years. Mathematical models for infectious diseases play a critical role in predicting and understanding disease mechanisms, and have long provided basic insights in the possible ways to control infectious diseases. In this paper, we present a new deterministic cholera epidemiological model with three types of control measures incorporated into a cholera epidemic setting: treatment, vaccination and sanitation. Essential dynamical properties of the model with constant intervention controls which include local and global stabilities for the equilibria are carefully analyzed. Further, using optimal control techniques, we perform a study to investigate cost-effective solutions for time-dependent public health interventions in order to curb disease transmission in epidemic settings. Our results show that the basic reproductive number (R0) remains the model's epidemic threshold despite the inclusion of a package of cholera interventions. For time-dependent controls, the results suggest that these interventions closely interplay with each other, and the costs of controls directly affect the length and strength of each control in an optimal strategy.