DETERMINISTIC AND STOCHASTIC MODELS OFINFECTIOUS DISEASES; SPECIAL STUDY OF COVID-19, DENGUE INFECTION, AND ZIKA INFECTION

• Main Author: Zevika, Mona
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/71453
• Institution: Institut Teknologi Bandung

Covid-19 infection and DHF are known as endemic diseases in Indonesia which have affected almost all cities in the country. With the same transmitting vectors for dengue and zika, it is important to understand the potential of zika outbreak in Indonesia. Covid-19 is known as a directly infectious disease that spread among humans with a high mortality rate during the world pandemic for the last 2 years. On the other hand, dengue infection is included in the list of the top ten causes of death in the world. Zika infection and dengue infection have many similarities, both diseases are caused by viruses and are spread by mosquitoes of the genus Aedes from human to human. So far, Zika infection is not a disease with a high mortality rate, but Zika infection can trigger the Guillain-Barr e Syndrome which is a brain disorder in adults and affect pregnant women at risk of giving birth to babies with microcephaly defects. In this dissertation, models of the spread of Covid-19, dengue infection, and Zika infection are studied with two approaches, namely deterministic and stochastic. The first model studies the spread of Covid-19 infection by developing the classic SIR model into SVEIQR. This model includes factors to prevent the spread of disease, namely the quarantine program and the vaccine program. In addition, the vaccine efficacy, the immune period due to the vaccine, and the natural immune period from Covid-19 infection are also temporary. The spread of Covid-19 was studied using two models, namely the deterministic model and the stochastic model. Analytically, two thresholds were obtained from these two models. The basic reproduction ratio as a deterministic model threshold was calculated using the next-generation matrix method. Meanwhile, the probability of disease extinction as a threshold for the CTMC stochastic model was calculated using the branching process. Numerical simulation shows the occurrence of endemic in the long term with the probability of disease extinction close to zero for the condition R0 > 1. This model study shows that vaccination programs and quarantine programs can reduce the number of new infection cases. In addition, efforts to increase vaccine efficacy are important things that need attention to deal with endemics that will occur in the long term. The second model studies the SEIR-SEI epidemic model which is suitable for the spread of dengue infection and Zika infection. In this model, analysis is given for preventing disease transmission, namely by using mosquito repellent solutions and fogging programs. This model was developed using two approaches, namely deterministic and stochastic, where each threshold is the basic reproduction ratio and the probability of disease extinction. The basic reproduction ratio is obtained analytically from the spectral radius next generation matrix, while the extinction probability is obtained analytically from the fixed point of the probability generating function of the branching process. The results of the model study show the relationship between the probability of disease extinction and the basic reproduction ratio. This model study shows that fogging is more effective than the use of mosquito repellent solutions in terms of decreasing the basic reproduction ratio and increasing the probability of disease extinction. The third model studies the coinfection of dengue infection and Zika infection in a population. In this model, it is assumed that there are two types of infection in one population simultaneously, namely dengue infection and Zika infection. This model was developed from the SIR-SI epidemic model with a deterministic approach. In this model, there are four equilibrium points, where the disease-free equilibrium, dengue boundary equilibrium, and Zika boundary equilibrium can be calculated explicitly, while the coinfection point cannot be calculated explicitly. The basic reproduction ratio was obtained analytically using the next-generation matrix method. In this study, R0 plays an important role in determining the extent of existence and stability of the four critical points. The complexity of the model limits the analysis of the model, so the exploration of the stability of coinfection points is carried out numerically with limited cases. The results showed that in asymmetrical cases, there was a Hopf bifurcation at the coinfection point and a limit cycle.