Effect of pollution on dynamics of SIR model with treatment

Chauhan, Sudipa; Bhatia, Sumit Kaur; Gupta, Surbhi

doi:10.1142/s1793524515500837

Cited by 11 publications

(6 citation statements)

References 19 publications

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“…This affects abundance of the host population and thus disease prevalence. Majority of theoretical studies which tried to address the impact of chemical pollution on disease however neglected these effects (Sinha et al, 2010;Liu et al, 2012;Chauhan et al, 2015;Wang and Ma, 2004). Although a recent study by Banerjee et al (2019) on a Daphnia-algae-fungus system took into consideration some of these aspects, it has few shortcomings.…”

Section: Introductionmentioning

confidence: 99%

Environmental toxicity influences disease spread in consumer population

Chattopadhyay¹,

Banerjee²,

Samadder³

et al. 2022

Preprint

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The study of infectious disease has been of interest to ecologists since long. The initiation of epidemic and the long term disease dynamics are largely influenced by the nature of the underlying consumer (host)-resource dynamics. Ecological traits of such systems may be often modulated by toxins released in the environment due to ongoing anthropogenic activities. This, in addition to toxin-mediated alteration of epidemiological traits, has a significant impact on disease progression in ecosystems which is quite less studied. In order to address this, we consider a mathematical model of disease transmission in consumer population where multiple traits are affected by environmental toxins. Long term dynamics show that the level of environmental toxin determines disease persistence, and increasing toxin may even eradicate the disease in certain circumstances. Furthermore, our results demonstrate bistability between different ecosystem states and the possibility of an abrupt transition from disease-free coexistence to disease-induced extinction of consumers. Overall the results from this study will help us gain fundamental insights into disease propagation in natural ecosystems in the face of present anthropogenic changes.

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Section: Introductionmentioning

confidence: 99%

Environmental toxicity influences disease spread in consumer population

Chattopadhyay¹,

Banerjee²,

Samadder³

et al. 2022

Preprint

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“…However, this proportionality is not satisfied in the reality because of limited medical facilities (see [19]). In order to include the limited capacity of medical resources, Chauhan et al,in [20], considered the piecewise linear treatment function of the form…”

Section: Introductionmentioning

confidence: 99%

“…where a represents the maximal medical resources supplied per united time and is half-saturation constant, which measures the effect of being delayed for treatment. Other works have investigated the effects of the treatment on an epidemic (see [19][20][21][22][23][24][25]) and also its optimal control (see [26]). The motivation of this work comes from [10,11], where the authors studied an SIR epidemic model with nonlinear incidence function, and from [19][20][21], where the authors considered a special type of treatment function.…”

Section: Introductionmentioning

confidence: 99%

Global stability analysis for a generalized delayed SIR model with vaccination and treatment

et al. 2019

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In this work, we investigate the stability of an SIR epidemic model with a generalized nonlinear incidence rate and distributed delay. The model also includes vaccination term and general treatment function, which are the two principal control measurements to reduce the disease burden. Using the Lyapunov functions, we show that the disease-free equilibrium state is globally asymptotically stable if R 0 ≤ 1, where R 0 is the basic reproduction number. On the other hand, the disease-endemic equilibrium is globally asymptotically stable when R 0 > 1. For a specific type of treatment and incidence functions, our analysis shows the success of the vaccination strategy, as well as the treatment depends on the initial size of the susceptible population. Moreover, we discuss, numerically, the behavior of the basic reproduction number with respect to vaccination and treatment parameters. MSC: 34D03; 92D30

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“…To conduct experiments and public health decisionmaking for solving this worldwide issue, mathematical models become one of the powerful tools for investigating infectious diseases [5], which have been used to provide useful insights into control measures [6][7][8][9]. For example, Wang and Ma [6] considered an SIS model in a polluted environment and obtained the persistence and periodic orbits of the model.…”

Section: Introductionmentioning

confidence: 99%

“…They analyzed the model by showing the positive invariance, existence and stability of equilibria, and bifurcations. Chauhan et al [9] considered an SIR epidemic model with treatment affected by pollution. Zhao et al [10] considered a stochastic susceptibleinfective epidemic model in a polluted environment, which incorporates both environmental fluctuations and pollution.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Stochastic Susceptible‐Infective Epidemic Model in a Polluted Atmospheric Environment

Zhao

Chen

2019

Complexity

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Atmospheric pollution is deteriorating, which has affected the evolution of respiratory disease for the exposed human worldwide. Thus, exploring the influence of air pollution on the evolution of disease transmission dynamics is a significant issue. In this article, a stochastic susceptible-infective (SI) epidemic model in a polluted atmospheric environment is investigated. The existence and uniqueness of the global positive solution are established. In virtue of the aggregation methods and Lyapunov function, the sufficient conditions of disease extinction, persistence, and existence of the stationary distribution are established, respectively. Taking PM2.5 concentration as the air pollutant index, numerical simulations are carried out to support these results. Our results indicated that the disease transmission dynamics (extinction, persistence, and stationary distribution) are significantly associated with the environmental atmospheric pollution and fluctuation.

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Effect of pollution on dynamics of SIR model with treatment

Cited by 11 publications

References 19 publications

Environmental toxicity influences disease spread in consumer population

Environmental toxicity influences disease spread in consumer population

Global stability analysis for a generalized delayed SIR model with vaccination and treatment

Analysis of a Stochastic Susceptible‐Infective Epidemic Model in a Polluted Atmospheric Environment

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