A delayed epidemic model of diseases through droplet infection and direct contact with saturation incidence and pulse vaccination

Abstract

In 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 R 1 and R 2. It is proved that there exists an infection-free periodic solution which is globally attractive if R 1 < 1 and the disease is permanent if R 2 > 1. 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.

Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

“…For example, one may construct some more realistic but complex models, such as considering the effects of delay, complex network, pulse vaccination and Lévy noise. Some scholars have already done a great deal of work (see [34][35][36][37][38][39][40]). We leave these investigations for future work.…”

An Seir Model With Infectious Latent and a Periodic Vaccination Strategy

“…In these models there are two different infected stages with different ability of transmitting the diseases [24,25,28]. Also Samanta et al [26] studied a delayed epidemic model with different constant contact rates.…”

Synthetic Drugs Transmission: Stability Analysis and Optimal Control

“…By forming epidemic models, one mainly tries to simulate and reveals the nature of epidemics and provides theoretical rules and results for preventing and controlling diseases (www.nncc626.com/2016-02/18/c 128731173 2.html., www.nncc626.com.) (Cen, Feng, & Zhao, 2014;Fang, Li, Martcheva, & Cai, 2014;Feng, Cen, Zhao, & Velasco-Hernandez, 2015;Huo, Chen, & Wang, 2016;Mulone & Straughan, 2009;Mushanyu, Nyabadza, & Stewart, 2015;Nyabadza, Njagarah, & Smith, 2013;Saha & Samanta, 2019a, 2019bSamanta, 2011;Samanta, Sen, & Maiti, 2016;White & Comiskey, 2007). White and Comiskey (2007) first studied a simple heroin model where the authors divided the total population into susceptible, heroin addicts who were not in treatment and heroin addicts who were under treatment.…”