An epidemic model of childhood disease dynamics with maturation delay and latent period of infection

Abstract

In the present study, an epidemic model is proposed with maturation delay and latent period of infection, keeping in view the childhood disease dynamics and studied the asymptotic behavior of the model for all the feasible equilibrium states. The criterion for local stability of the system around steady states are established in terms of delay, latent period and system parameters. Further explored the possibility of Hopf bifurcation at the endemic equilibrium state and threshold is determined. We also performed the sensitivity analysis of the state variables at the endemic equilibrium state with respect to the model parameters and identified the respective sensitive indices. Further numerical simulations have been carried out to justify our analytic findings.

Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases

“…Measles, poliomyelitis, and rubella are famous among them [1,2]. Measles is a highly infectious disease, caused by respiratory infection by a Morbillivirus.…”

“…Mathematical model plays an important role to comprehend the process of transmission of a disease and provides different techniques to control its propagation. Many mathematicians investigated childhood disease; for instance, Singh et al [2] studied about vaccination of the childhood diseases. In addition, the authors presented numerical solution of the childhood disease model.…”

Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

“…The mathematical model plays an important comprehend the process of transmission disease and provides different techniques to control propagation. Many mathematicians investigated childhood disease; for instance, Henderson et al [Henderson (1984); Singh, Dhar, Bhatti et al (2016)] studied the diseases vaccination of childhood. Makinde [Makinde (2007)] presented the Susceptible-Infected-Recovered.…”

“…Many applications of science and engineering the nonlinear equations appear such as fluid dynamics, plasma physics, hydrodynamics, solid-state physics, optical fibers, acoustics and other disciplines [Adomian (1994)]. The analyatic and approximate solutions many effective methods for obtaining to the NPDEs among of these methods are discussed in Ablowitz et al [Ablowitz and Clarkson (1991); Singh, Dhar, Bhatti et al (2016)]. In the present article, we use the reduced differential transform method (RDTM) which discussed in ; ]; [Amer, Mahdy and Youssef (2018)], to construct an approximate numerical solution of some highly nonlinear differential equations in biomathematics.…”

An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets

“…Presently childhood diseases are most significant infectious diseases. Rubella, measles, poliomyelitis, and hepatitis B have serious concerns among them [2][3][4][5][6][7]. Recently, coronavirus diseases have been discussed in [8].…”