Modelling the spread of carrier-dependent infectious diseases with environmental effect

Ghosh, Mini; Chandra, Peeyush; Sinha, Prawal; Shukla, J.B.

doi:10.1016/s0096-3003(03)00564-2

Cited by 36 publications

(30 citation statements)

References 11 publications

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“…The functions f 1 (I) and f 2 (B) depict the direct and indirect transmission rates, respectively. For example, f 1 (I) = 0 and f 2 (B) = aB/(B + κ) in the model of Codeco [7] (where a is the contact rate with contaminated water, and κ is the half saturation rate that describes the infectious dose in water sufficient to produce disease in 50% of those exposed), f 1 (I) = βI and f 2 (B) = λB in the model proposed by Gosh et al [11] (where β and λ represent the direct and indirect transmission parameters due to the human-to-human and the environment-to-human interactions, respectively), and f 1 (I) = β h I and f 2 (B) = β e B/(B + κ) in the model of Mukandavire et al [22] (where β h and β e represent the direct and indirect transmission parameters). In addition, d is the natural death rate of each host class, γ is the recovery Figure 1.…”

Section: Model Descriptionmentioning

confidence: 99%

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Analysis of cholera epidemics with bacterial growth and spatial movement

Wang

2014

Journal of Biological Dynamics

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In this work, we propose novel epidemic models (named, susceptible-infected-recovered-susceptiblebacteria) for cholera dynamics by incorporating a general formulation of bacteria growth and spatial variation. In the first part, a generalized ordinary differential equation (ODE) model is presented and it is found that bacterial growth contributes to the increase in the basic reproduction number, R 0 . With the derived basic reproduction number, we analyse the local and global dynamics of the model. Particularly, we give a rigorous proof on the endemic global stability by employing the geometric approach. In the second part, we extend the ODE model to a partial differential equation (PDE) model with the inclusion of diffusion to capture the movement of human hosts and bacteria in a heterogeneous environment. The disease threshold of this PDE model is studied again by using the basic reproduction number. The results on the threshold dynamics of the ODE and PDE models are compared, and verified through numerical simulation. Additionally, our analysis shows that incorporating diffusive spatial spread does not produce a Turing instability when R 0 associated with the ODE model is less than the unity.

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Section: Model Descriptionmentioning

confidence: 99%

“…The incidence functions employed in most of the existing cholera models (e.g. [7,11,22,35]) satisfy these conditions. Meanwhile, the assumption (H3) states that the bacterial growth rate is also subject to saturation effects.…”

Section: Model Descriptionmentioning

confidence: 99%

Analysis of cholera epidemics with bacterial growth and spatial movement

Wang

2014

Journal of Biological Dynamics

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“…Hence, it is sufficient to consider the dynamics of the flow generated by (2) in D. In this region, the model can be considered as being epidemiologically and mathematically well posed [12]. Thus, every solution of the basic model (2) with initial conditions in D remains in D for all t > 0.…”

Section: Invariant Regionsmentioning

confidence: 99%

“…The DFE of the model (2), given by R s , is locally asymptotically stable (LAS) if R s < 1, and unstable if R s > 1.…”

Section: Theoremmentioning

confidence: 99%

“…For instance, the study of an infectious disease model with population-dependent death rate using computer simulation was investigated by Greenhalgh [1]. To examine the impact of climate on disease spread, Ghosh et al [2], studied the environmental effect on an SIS model for bacteria and the spread of carrierdependent infectious diseases, like cholera and diarrhea. Anderson and May [3] derived a deterministic malaria model to investigate the effect of acquired immunity in malaria and different control measures on the transmission rate and on the disease prevalence.…”

Section: Introductionmentioning

confidence: 99%

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On a drug-resistant malaria model with susceptible individuals without access to basic amenities

Okosun

Makinde

2012

J Biol Phys

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In this paper, a deterministic malaria transmission model in the presence of a drug-resistant strain is investigated. The model is studied using stability theory of differential equations, optimal control, and computer simulation. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved in the absence of a drug-resistant strain in the population. The existence of multiple endemic equilibria is also established. Both the Sensitivity Index (SI) of the model parameters and the Incremental Cost-Effectiveness Ratio (ICER) for all possible combinations of the disease-control measures are determined. Our results revealed among others that the most cost-effective strategy for drug-resistant malaria control is the combination of the provision of basic amenities (such as access to clean water, electricity, good roads, health care, and education) and treatment of infective individuals. Therefore, more efforts from policy-makers on the provisions of basic amenities and treatment of infectives would go a long way to combat the malaria epidemic.

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An SIR Model with Nonlinear Incidence Rate and Holling Type III Treatment Rate

Dubey

2016

Applied Analysis in Biological and Physical Sciences

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Modelling the spread of carrier-dependent infectious diseases with environmental effect

Cited by 36 publications

References 11 publications

Analysis of cholera epidemics with bacterial growth and spatial movement

Analysis of cholera epidemics with bacterial growth and spatial movement

On a drug-resistant malaria model with susceptible individuals without access to basic amenities

An SIR Model with Nonlinear Incidence Rate and Holling Type III Treatment Rate

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