The Effects of Fogging and Mosquito Repellent on the Probability of Disease Extinction for Dengue Fever

A Continuous-Time Markov Chain model is constructed based on the a deterministic model of dengue fever transmission including mosquito fogging and the use of repellent. The basic reproduction number (R0) for the corresponding deterministic model is obtained. This number indicates the possible occurrence of an endemic at the early stages of the infection period. A multitype branching process is used to approximate the Markov chain. The construction of offspring probability generating functions related to the infected states is used to calculate the probability of disease extinction and the probability of an outbreak (P0). Sensitivity analysis is shown for variation of control parameters and for indices of the basic reproduction number. These results allow for a better understanding of the relation of the basic reproduction number with other indicators of disease transmission

A Particle System Model for Dengue Transmission

Dengue disease has been known for decades as a vector-borne disease which is rapidly spreading in many tropical and subtropical countries. The disease is transmitted mostly by female Aedes aegypty mosquitoes. Although detailed biological properties of the infection process are already known, in the field applications the disease transmission of dengue is still far from being successfully controlled. The complexity surrounding the transmission is contributed by various factors such as climate, mobility and human-mosquito behavior. Many deterministic models have been developed to investigate the spread of dengue. However, in a deterministic model, spatial heterogeneity factor is not considered. In fact, distances between people and mosquitoes greatly influence the spread of dengue. This paper discusses a microscopic model of the spread of dengue based on spatial heterogeneity. In this microscopic model, every human and mosquito is regarded as a particle and the corresponding human and mosquito populations with their health status are considered as a system of particles. Three important dynamical factors and processes are constructed for each particle, i.e., position and health status of each particle, natural birth and death, infection and transition processes. An estimate of the corresponding basic reproductive ratio is introduced to accommodate the variation of health status and spatial spread of particle

On The Study of Covid-19 Transmission Using Deterministic and Stochastic Models with Vaccination Treatment and Quarantine

In this study, we propose deterministic and stochastic models of the spread of Covid-19 with vaccination and quarantine programs. The model considers the facts that vaccines do not provide full protection, the efficacy of current vaccines only lasts for a limited time, and recovered people could be reinfected. The routine analysis was carried out for the deterministic model, including calculating an expression for the basic reproduction number. The stochastic formulation makes use of a Continuous-Time Markov Chain (CTMC) model. The basic reproduction number from the deterministic model relates to the stochastic model's analysis in producing a formula for the probability of extinction of Covid-19. Furthermore, numerical simulations are carried out to analyze the sensitivity of the dynamical states and the basic reproduction number to the model parameters. An expression for the probability of disease extinction in terms of the model parameters and initial conditions is given. The results of this study suggest that current conditions in Indonesia will lead to a longterm Covid-19 epidemic. One of the efforts to overcome the Covid-19 epidemic is by increasing the provision of vaccines to the susceptible population. However, the number of vaccinated people in the population is not always an ideal control for dealing with the spread of the disease. The vaccine efficacy is also important to reduce the infection. As long as the efficacy is not sufficient to give a good protection to the human population and it lasts only for a short period of time, quarantine is still needed

Implementation of Online Think Pairs Share (OTPS) Model to Improve Student Learning Outcome

This study was an online classroom action research (PTK) due to the COVID-19 pandemic. This study aimed to improve learning outcomes in calculus classes for physics engineering students using think pairs share. The online think pairs share (OTPS) learning model was optimized using the Learning Management System (LMS) platform in two learning cycles. The research sample was 46 students in the study program of physics engineering. The data were obtained from the pre-test-post-test scores, group discussions, and individual presentations. The results showed that the pre-test and post-test scores in cycle I were 37.16 and 68.41, while in cycle II, 41.20 and 68.65, respectively. In addition, the daily student score from the group discussion and individual presentation was 60.68 for the cycle I and 60.15 for cycle II. Furthermore, inferential analysis using the Kolmogorov-Smirnov test proves that tcount > ttable. Hence, the result indicated that implementing the OTPS learning model optimized using LMS could improve the student learning outcomes in calculus