Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment

Rajasekar, S.; Pitchaimani, M.; Zhu, Quanxin

doi:10.1016/j.physa.2019.122649

Cited by 31 publications

(15 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In reality, the environmental noise perverts through and medal with the population dynamics, ecology, environmental sciences, and mathematical biology. Stochasticity has its impact upon various biological [18][19][20][21][22][23][24][25] and other models [26][27][28][29][30]. Many researchers probed stochastic tuberculosis models in which the total host population can be divided into three, four, and five epidemiological classes, respectively, such as susceptible (S), exposed (E), and infected (I) [31]; susceptible (S), latent (L), infectious (I), and treated (T) [32]; susceptible (S), exposed (E), infected (I), and recovered (R) [33]; and susceptible (S), vaccinated (V), infected with TB in latent stage (L), infected with TB in active stage (I), and treated individuals infected with TB (T) [34,35].…”

Section: Introductionmentioning

confidence: 99%

Exploring the Stochastic Host-Pathogen Tuberculosis Model with Adaptive Immune Response

Rajasekar

Pitchaimani

Zhu

et al. 2021

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

In this literature, we probe a stochastic host-pathogen tuberculosis model with the adaptive immune response of four states of epidemiological classification: Mycobacterium tuberculosis, uninfected macrophages, infected macrophages, and immune response CD4+ T cells. This model is pertinent to the latent stage of tuberculosis infection and active tuberculosis-infected individuals. The stochastic host-pathogen tuberculosis model in pathology is constituted based on the environmental influence on the Mycobacterium tuberculosis and macrophage population, elucidated by stochastic perturbations, and it is proportional to each state. We evince the existence and a unique global positive solution of a stochastic tuberculosis model. We attain sufficient conditions for the extinction of the tubercle bacillus. Moreover, we acquire the existence of the stationary distribution of the positive solutions by the Lyapunov function method. Eventually, numerical simulations validate analytical findings and the dynamics of the stochastic TB model.

show abstract

Section: Introductionmentioning

confidence: 99%

Exploring the Stochastic Host-Pathogen Tuberculosis Model with Adaptive Immune Response

Rajasekar

Pitchaimani

Zhu

et al. 2021

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…For example, Schurz [14] considered a fairly general version of the stochastic differential equation associated with logistic growth, and Rupšys [15] introduced several versions of the differential equation that included delays, whereas Schlomann [16] studied logistic diffusion processes in the presence of catastrophes. This field is unceasingly producing new research, as exemplified by the recent works of Rajasekar et al [17,18] in which the authors analyzed a stochastic version of the SIR models for the spread of the COVID-19 pandemic. On the other hand, the fact that the Gompertz curve is an excellent model for the description of tumor growth has motivated the introduction of several diffusion processes associated with it (see, for example, Lo [19] and Ferrante [20]).…”

Section: Introductionmentioning

confidence: 99%

Hyperbolastic Models from a Stochastic Differential Equation Point of View

2021

View full text Add to dashboard Cite

A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of the Malthusian type. By virtue of this, and by adding a multiplicative noise to said ordinary differential equation, a diffusion process may be associated with each curve whose mean function is said curve. The inference in the resulting processes is presented jointly, as well as the strategies developed to obtain the initial solutions necessary for the numerical resolution of the system of equations resulting from the application of the maximum likelihood method. The common perspective presented is especially useful for the implementation of the necessary procedures for fitting the models to real data. Some examples based on simulated data support the suitability of the development described in the present paper.

show abstract

“…It elaborates the overall effects that occur due to the behavioral change of susceptible from the crowding effect of the infective individuals, vice versa. In addition to this property, it prevents the unboundedness of the contact rate by choosing suitable parameters [19] , [20] , [21] , [22] , [23] , [24] . Therefore, the representation of incidence rate using Holling type II function is more reasonable than the bilinear incidence rate.…”

Section: Introductionmentioning

confidence: 99%

Behavioral response of population on transmissibility and saturation incidence of deadly pandemic through fractional order dynamical system

et al. 2021

View full text Add to dashboard Cite

The world entered in another wave of the SARS-CoV-2 due to non-compliance of standard operating procedures appropriately, initiated by respective governments. Apparently, measures like using face masks and social distancing were not observed by populace that ultimately worsens the situation. The behavioral response of the population induces a change in the dynamical outcomes of the pandemic, which is documented in this paper for all intents and purposes. The innovative perception is executed through a compartmental model with the incorporation of fractional calculus and saturation incident rate. In the first instance, the epidemiological model is designed with proportional fractional definition considering the compartmental individuals of susceptible, social distancing, exposed, quarantined, infected, isolated and recovered populations. By virtue of proportional fractional derivative, effective dynamical outcomes of equilibrium states and basic reproduction number are successfully elaborated with memory effect. The expansion of this derivative greatly simplifies the model to integer order while remaining in the fractional context. Subsequently, the memory effects on the asymptotic profiles are demonstrated through various graphical plots and tabulated values. In addition, the inclusion of saturation incident rate further explains the transmissibility of infection for different behavior of susceptible individuals. Mathematically, the results are also validated through comparative analysis of values with the solutions attained from fractional fourth order Runge-Kutta method (FRK4).

show abstract

Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment

Cited by 31 publications

References 27 publications

Exploring the Stochastic Host-Pathogen Tuberculosis Model with Adaptive Immune Response

Exploring the Stochastic Host-Pathogen Tuberculosis Model with Adaptive Immune Response

Hyperbolastic Models from a Stochastic Differential Equation Point of View

Behavioral response of population on transmissibility and saturation incidence of deadly pandemic through fractional order dynamical system

Contact Info

Product

Resources

About