Mathematical transmission analysis of SEIR tuberculosis disease model

Abstract Tuberculosis is one of the burning issues of the modern era that causes serious health hazard in human body in last few decades. In this article, we proposed and analyzed the SEIR pandemic TB transmission model with time subordinate boundaries. We considered a compartmental TB mathematical model where the total population is ordered into four compartments as indicated by their natural highlights. We explored the effect of different phases of the compartments by analyzing the infection at free stability point along with basic reproduction, strength of the system and at endemic stability point. It is indicated that the TB model is locally as well as globally asymptotically stable at infection free stability point when the basic reproduction number is not as much as unity and novel endemic harmony when the basic reproduction number is more prominent than unanimity. A bifurcation investigation is performed by applying the bifurcation technique tools of the centre manifold theory. Mathematical conditions guarantee the event of forward bifurcation which has been inferred.

[1]  S. Pinelas,et al.  Stability of the Zero Solution of Nonlinear Tumor Growth Cancer Model under the Influence of White Noise , 2018 .

[2]  Fei Li,et al.  Dynamics Analysis of a Nonlinear Stochastic SEIR Epidemic System with Varying Population Size , 2018, Entropy.

[3]  D. Rock.  Tuberculosis: a global emergency. , 1997, Work.

[4]  C. Castillo-Chavez,et al.  Transmission and dynamics of tuberculosis on generalized households. , 2000, Journal of theoretical biology.

[5]  Eric Sarkodie.  Modeling the spread of tuberculosis in Central Region using the susceptible-exposed-infected-susceptible (SEIS) mathematical model , 2014 .

[6]  Robert H. Martin.  Logarithmic norms and projections applied to linear differential systems , 1974 .

[7]  Christopher Dye,et al.  Evolution of tuberculosis control and prospects for reducing tuberculosis incidence, prevalence, and deaths globally. , 2005, JAMA.

[8]  Deborah Lacitignola,et al.  Global stability of an SIR epidemic model with information dependent vaccination. , 2008, Mathematical biosciences.

[9]  Deborah Lacitignola,et al.  On the backward bifurcation of a vaccination model with nonlinear incidence , 2011 .

[10]  C. Castillo-Chavez,et al.  A model for tuberculosis with exogenous reinfection. , 2000, Theoretical population biology.

[11]  G. Tilahun,et al.  Stochastic model of measles transmission dynamics with double dose vaccination , 2020, Infectious Disease Modelling.

[12]  E. Bloss,et al.  Under-reporting of sputum smear-positive tuberculosis cases in Kenya. , 2016, The international journal of tuberculosis and lung disease : the official journal of the International Union against Tuberculosis and Lung Disease.

[13]  Zhien Ma,et al.  Global dynamics of an SEIR epidemic model with saturating contact rate. , 2003, Mathematical biosciences.

[14]  Michael Y. Li,et al.  Global stability for the SEIR model in epidemiology. , 1995, Mathematical biosciences.

[15]  Zhidong Teng,et al.  An SIRVS epidemic model with pulse vaccination strategy. , 2008, Journal of theoretical biology.

[16]  Toshikazu Kuniya,et al.  Global dynamics of a class of SEIRS epidemic models in a periodic environment , 2010 .

[17]  Carlos Castillo-Chavez,et al.  Markers of disease evolution: the case of tuberculosis. , 2002, Journal of theoretical biology.

[18]  M. Islam,et al.  Mathematical modeling of hepatitis B virus infection incorporating immune responses , 2020 .

[19]  Carlos Castillo-Chavez,et al.  Mathematical approaches for emerging and reemerging infectious diseases , 2002 .

[20]  Andrei Korobeinikov,et al.  Lyapunov functions and global properties for SEIR and SEIS epidemic models. , 2004, Mathematical medicine and biology : a journal of the IMA.

[21]  Xinyu Song,et al.  Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function , 2014, TheScientificWorldJournal.

[22]  M. Gani,et al.  Modeling the dispersal effect to reduce the infection of COVID-19 in Bangladesh , 2020, Sensors International.

[23]  Robert J. Smith,et al.  Modelling the daily risk of Ebola in the presence and absence of a potential vaccine , 2020, Infectious Disease Modelling.

[24]  T. Britton,et al.  SEIRS epidemics with disease fatalities in growing populations. , 2018, Mathematical biosciences.

[25]  Carlos Castillo-Chavez,et al.  Dynamical models of tuberculosis and their applications. , 2004, Mathematical biosciences and engineering : MBE.

[26]  Md. Haider Ali Biswas,et al.  A SEIR model for control of infectious diseases with constraints , 2014 .

[27]  Diffusion Dynamics and Impact of Noise on a Discrete-Time Ratio-Dependent Model: An Analytical and Numerical Approach , 2019 .

[28]  Sensitivity and elasticity analysis of novel corona virus transmission model: A mathematical approach , 2021, Sensors International.

[29]  Kalyan Das,et al.  Chaotic dynamics of a three species prey-predator competition model with noise in ecology , 2014, Appl. Math. Comput..

[30]  H. A. Biswas,et al.  Discrete Type SIR Epidemic Model with Nonlinear Incidence Rate in Presence of Immunity , 2020, WSEAS TRANSACTIONS ON BIOLOGY AND BIOMEDICINE.

[31]  Mostafa M. A. Khater,et al.  Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions , 2018, Mathematical and Computational Applications.

[32]  K B Blyuss,et al.  Mathematical model for the impact of awareness on the dynamics of infectious diseases. , 2017, Mathematical biosciences.

[33]  P. Giles,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .