Abstract
Epidemiological models have been playing a vital role in different areas of biological sciences for the analysis of various contagious diseases. Transmissibility of virulent diseases is being portrayed in the literature through different compartments such as susceptible, infected, recovered (SIR), susceptible, infected, recovered, susceptible (SIRS) or susceptible, exposed, infected, recovered (SEIR), etc. The novelty in this endeavor is the addition of compartments of latency and treatment with vaccination, so the system is designated as susceptible, vaccinated, exposed, latent, infected, treatment, and recovered (SVELITR). The contact of a susceptible individual to an infective individual firstly makes the individual exposed, latent, and then completely infection carrier. Innovatively, the assumption that exposed, latent, and infected individuals enter the treatment compartment at different rates after a time lag is also deliberated through the existence of time delay. The rate of change and constant solutions of each compartment are studied with incorporation of a special case of proportional fractional derivative (PFD). In addition, existence and uniqueness of the system are also comprehensively elaborated. Moreover, novel dynamic assessment of the system is carried out in context with the fractional order index. Succinctly, the manuscript accomplishes cyclic epidemiological behavior of the infectious disease due to the delay in treatment of the infected individuals.
Highlights
Mathematical modelling is a significant tool in epidemiology that helps healthcare researchers and policymakers to make public health and socioeconomic decisions
A tremendous number of models have been formulated, analyzed, and applied, which improved our understanding and predictive ability about a variety of infectious diseases [1,2,3,4,5]. Many of these models consider time delay in the process of transmissibility of any infection to further study the effect of delays on the spread out of diseases
Zhang et al [7] generated significant results elaborating the influence of time delay on the stability and measures of synthetic drugs transmission
Summary
Mathematical modelling is a significant tool in epidemiology that helps healthcare researchers and policymakers to make public health and socioeconomic decisions. A tremendous number of models have been formulated, analyzed, and applied, which improved our understanding and predictive ability about a variety of infectious diseases [1,2,3,4,5] Many of these models consider time delay in the process of transmissibility of any infection to further study the effect of delays on the spread out of diseases. 2 comprises details of modelling the aforementioned assumptions with essential theorems All the remaining equations of system (6) can be ascertained to have nonnegative solutions with the assumption of positive initial conditions.
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