RESUMO
Dengue fever is a viral mosquito-borne infection and a major international public health concern. With 2.5 billion people at risk of acquiring the infection around the world, disease severity is influenced by the immunological status of the individual, seronegative or seropositive, prior to natural infection. Caused by four antigenically related but distinct serotypes, DENV-1 to DENV-4, infection by one serotype confers life-long immunity to that serotype and a period of temporary cross-immunity (TCI) to other serotypes. The clinical response on exposure to a second serotype is complex with the so-called antibody-dependent enhancement (ADE) process, a disease augmentation phenomenon when pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection, used to explain the etiology of severe disease. In this paper, we present a minimalistic mathematical model framework developed to describe qualitatively the dengue immunological response mediated by antibodies. Three models are analyzed and compared: (i) primary dengue infection, (ii) secondary dengue infection with the same (homologous) dengue virus and (iii) secondary dengue infection with a different (heterologous) dengue virus. We explore the features of viral replication, antibody production and infection clearance over time. The model is developed based on body cells and free virus interactions resulting in infected cells activating antibody production. Our mathematical results are qualitatively similar to the ones described in the empiric immunology literature, providing insights into the immunopathogenesis of severe disease. Results presented here are of use for future research directions to evaluate the impact of dengue vaccines.
RESUMO
Measles is a contagious disease caused by the measles virus of genus Morbillivirus, which has been spreading in many affected regions. This infection is characterized by the appearance of rashes all over the body and potentially cause serious complications, especially among infants and children. Before measles immunization was promoted, it is one of the endemic diseases that caused the most fatalities each year in the world. This paper aims to analyze and to investigate measles transmission in Jakarta via an SIHR epidemic model involving vaccination from January to December 2017. Jakarta Health Office collected the observed data of measles incidence. We then derived the basic reproduction number as a threshold of disease transmission and obtained the local as well as global stability of the equilibria under certain conditions. The unobserved parameters and initial conditions were estimated by minimizing errors between data and numerical results. Furthermore, a stochastic model was developed to capture the data and to accommodate the randomness of the transmission. Sensitivity analysis was also performed to analyze and to identify the parameters which give significant contributions to the spread of the virus. We then obtained simulations of vaccine level coverage. The data is shown within a 95% confidence interval of the stochastic solutions, and the average of the stochastic solutions is relatively close to the solution of the deterministic model. The most sensitive parameter in the infected compartment is the hospitalized rate, which can be considered to be one of the essential factors to reduce the number of cases for policymakers. We hence proposed a control strategy which is providing treatment accesses easier for infected individuals is better than vaccinating when an outbreak occurs.
