Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function

Dengue is one of the major health problems in Bangladesh and many people are died in recent years due to the severity of this disease. Therefore, in this paper, a SIRS model for the human and SI model for vector population with saturated incidence rate and constant treatment function has been presented to describe the transmission of dengue. The equilibrium points and the basic reproduction number have been computed. The conditions which lead the disease free equilibrium and the endemic equilibrium have been determined. The local stability for the equilibrium points has been established based on the eigenvalues of the Jacobian matrix and the global stability has been analyzed by using the Lyapunov function theory. It is found that the stability of equilibrium points can be controlled by the reproduction number. In order to calculate the infection rate, data for infected human populations have been collected from several health institutions of Bangladesh. Numerical simulations of various compartments have been generated using MATLAB to investigate the influence of the key parameters for the transmission of the disease and to support the analytical results. The effect of treatment function over the infected compartment has been illustrated. The sensitivity of the reproduction number concerning the parameters of the model has been analyzed. Finally, the most sensitive parameter that has the highest effect over reproduction number has been identified

Dynamic model of COVID-19 disease with exploratory data analysis

Novel Coronavirus is a highly infectious disease, with over one million confirmed cases and thousands of deaths recorded. The disease has become pandemic, affecting almost all nations of the world, and has caused enormous economic, social and psychological burden on countries. Hygiene and educational campaign programmes have been identified to be potent public health interventions that can curtail the spread of the highly infectious disease. In order to verify this claim quantitatively, we propose and analyze a nonlinear mathematical model to investigate the effect of healthy sanitation and awareness on the transmission dynamics of Coronavirus disease (COVID-19) prevalence. Rigorous stability analysis of the model equilibrium points was performed to ascertain the basic reproduction number R 0 , a threshold that determines whether or not a disease dies out of the population. Our model assumes that education on the disease transmission and prevention induce behavioral changes in individuals to imbibe good hygiene, thereby reducing the basic reproduction number and disease burden. Numerical simulations are carried out using real life data to support the analytic results.http://www.elsevier.com/locate/sciafam2021Mathematics and Applied Mathematic

SIR Model for Dengue Disease with Effect of Dengue Vaccination

The dengue disease is caused by dengue virus, and there is no specific treatment. The medical care by experienced physicians and nurses will save life and will lower the mortality rate. A dengue vaccine to control the disease is available in Thailand since late 2016. A mathematical model would be an important way to analyze the effects of the vaccination on the transmission of the disease. We have formulated an SIR (susceptible-infected-recovered) model of the transmission of the disease which includes the effect of vaccination and used standard dynamical modelling methods to analyze the effects. The equilibrium states and their stabilities are investigated. The trajectories of the numerical solutions plotted into the 2D planes and 3D spaces are presented. The main contribution is determining the role of dengue vaccination in the model. From the analysis, we find that there is a significant reduction in the total hospitalization time needed to treat the illness