Role of Environmental Contamination in Measles Transmission dynamics

Abstract

Measles disease is one of the biggest communicable diseases and is still responsible for 2.598 million deaths every year. In this regard, our research focuses on measles disease transmission dynamics and the impact of indirect contact rates on the environment. In this paper, we propose a nonlinear mathematical model for measles disease and analyze a deterministic epidemiological measles model for control of the disease using vaccination. Here we executed the equilibrium points of the model, and we got two equilibrium points, namely, a disease-free equilibrium point (DEFP) and a unique endemic equilibrium point (EEP), and we also analyzed the local stability of DFEP and EEP by center manifold theory. Here we have also shown the global stability of DFEP and EEP by theCastillo-Chavez criterion and Lasalle invariant principle, respectively. In this study, we executed the basic reproduction number. if the basic reproduction number is less than unity otherwise the system shows a significant outbreak. Numerical illustrations demonstrate that if the rate of environmental contamination increased, then the number of infected people also increased. But if the environment is disinfected by sanitization then the number of infected people cannot drastically increase.