Abstract
ABSTRACTIn this paper, we have considered a dynamical model of diseases that spread by droplet infection and also through direct contact with varying total population size and discrete time delay to become infectious. It is assumed that there is a latent period of the disease and an immune period of the recovered individuals. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analysed this model with pulse vaccination and saturation incidence rate. It is also assumed that the time lag due to lose of immunity of recovered individuals is equal to the interval between two pulses. We have defined two positive numbers and . It is proved that there exists an infection-free periodic solution which is globally attractive if and the disease is permanent if The important mathematical findings for the dynamical behaviour of the model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically.
Highlights
Infectious diseases have tremendous influence on human life and are usually caused by pathogenic microorganisms, such as bacteria, viruses, parasites or fungi
In this paper we have considered a dynamical model of diseases that spread by droplet infection and through direct contact with pulse vaccination and saturation incidence rate
Because some successfully vaccinated susceptible individuals gradually lose their immunity after the bacterin is expired
Summary
Infectious diseases have tremendous influence on human life and are usually caused by pathogenic microorganisms, such as bacteria, viruses, parasites or fungi. Chickenpox is an airborne disease which spreads through coughing or sneezing of infectious individuals or through direct contact with secretions from the rash of an infectious person. Measles is a highly contagious viral disease and the virus causing it is spread by coughing and sneezing via close personal contact or direct contact with secretions. Samanta (2011) has proposed and analysed a nonautonomous dynamical model of diseases that spread by droplet infection and through direct contact with varying total population size and distributed time delay to become infectious. In this paper we have considered a dynamical model of diseases that spread by droplet infection and through direct contact with pulse vaccination and saturation incidence rate. It is assumed that the infection spreads through pathogens (bacteria and/or viruses) produced by droplets as well as by direct contact of individuals from infectious people.
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