Dynamics of a time-delayed SIR epidemic model with logistic growth and saturated treatment

Ávila-Vales, Eric; Pérez, Ángel

doi:10.1016/j.chaos.2019.06.024

Cited by 38 publications

(10 citation statements)

References 13 publications

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“…On the other hand, semi-annual models may not capture the fluctuations in disease dynamics as accurately as quarterly models, quarterly models can capture seasonal variations in disease transmission such as temperature and precipitation pikes 67 . This can be particularly useful for monitoring the effectiveness of interventions or identifying outbreaks before they become severe 68,69 . Where au is the biting rate described by the Human biting index 𝐻𝐵𝐼 𝑎 𝑢 = 𝐵𝑖𝑡𝑖𝑛𝑔 𝑟𝑎𝑡𝑒 = 𝐻𝐵𝐼 1 𝐵𝑀𝐷𝑅 And the BMDR is the Blood Meal digestion rate as a function of the temperature (T) described by the equation of the curve estimated from the data of [70][71][72] Consequently, the model accounts for temperature and precipitation by factoring in their impact on the biting rate au.…”

Section: Land Use Land Cover Temperature and Precipitationmentioning

confidence: 99%

Time-lagged response of malaria transmission to climate and land use change in a Colombian Amazonian Municipality: Implications for Early Warning Systems and Control Strategies

Gonzalez-Daza

Herrera

Altamiranda‐Saavedra

et al. 2023

Preprint

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Malaria remains a significant public health problem worldwide, particularly in low-income regions with limited access to healthcare. Despite the use of antimalarial drugs, transmission remains an issue in Colombia, especially among indigenous populations in remote areas. In this study, we used an SIR Ross MacDonald model that considered land use changes, temperature, and precipitation to analyze eco epidemiological parameters and the impact of time lags on malaria transmission in La Pedrera - Amazonas municipality. We found changes in land use between 2007 and 2020, with increases in forested areas, urban infrastructure and water edges area resulting in a constant increase in mosquito carrying capacity. Temperature and precipitation variables exhibited a fluctuating pattern that corresponded to rainy and dry seasons, respectively and a marked influence of the El Niño climatic phenomenon. Our findings suggest that elevated precipitation and temperature increase malaria infection risk in the following two months influenced by the secondary vegetation and urban infrastructure near primary forest formation or water body edges. These results may be useful for public health officials and policymakers in developing effective malaria control strategies by monitoring precipitation, temperature, and land use variables to predict high-risk areas and periods, considering the time lag effect.

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Section: Land Use Land Cover Temperature and Precipitationmentioning

confidence: 99%

Time-lagged response of malaria transmission to climate and land use change in a Colombian Amazonian Municipality: Implications for Early Warning Systems and Control Strategies

Gonzalez-Daza

Herrera

Altamiranda‐Saavedra

et al. 2023

Preprint

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“…[ 43 , 44 ], the incidence function g ( I ) gradually reaches a saturation level with the scale of infected individuals I increasing. Noticing the insightful effect of nonlinear incidence on epidemic dynamics, lots of authors [ 40 , 45 – 48 ] are devoted to studying the nonlinear dynamics of various epidemic models incorporated with saturated incidence rate. For instance, Zhu et al [ 48 ] perfectly explore the stability of equilibrium points and the effectiveness of control schemes in a delayed SIS epidemic model along with nonlinear incidence rate.…”

Section: Introductionmentioning

confidence: 99%

Stability behavior of a two-susceptibility SHIR epidemic model with time delay in complex networks

Guan

Guo

2021

Nonlinear Dyn

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Taking two susceptible groups into account, we formulate a modified subhealthy-healthy-infected-recovered (SHIR) model with time delay and nonlinear incidence rate in networks with different topologies. Concretely, two dynamical systems are designed in homogeneous and heterogeneous networks by utilizing mean field equations. Based on the next-generation matrix and the existence of a positive equilibrium point, we derive the basic reproduction numbers and which depend on the model parameters and network structure. In virtue of linearized systems and Lyapunov functions, the local and global stabilities of the disease-free equilibrium points are, respectively, analyzed when in homogeneous networks and in heterogeneous networks. Besides, we demonstrate that the endemic equilibrium point is locally asymptotically stable in homogeneous networks in the condition of . Finally, numerical simulations are performed to conduct sensitivity analysis and confirm theoretical results. Moreover, some conjectures are proposed to complement dynamical behavior of two systems.

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“…Noticing that compared with the traditional ordinary differential equation ODE [9][10][11][12], the delay differential equation DDE, which can reflect the system's state in the past specific time, is more practical [13][14][15][16]. Time delay plays a vital role in describing the dynamics of disease transmission.…”

Section: Introductionmentioning

confidence: 99%

Stability and optimal control strategy analysis for a class of SEIQR model with time delay on scale-free networks

Ma¹,

Wang²,

Cui³

2021

Phys. Scr.

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Numerous experiences in fighting epidemic diseases have revealed that isolation before treatment is an effective way to prevent the further spread of the epidemic, which scholars in current researches mostly ignore. Also, medical research shows that most infectious diseases have an incubation period, and the length of the incubation period will affect the final therapeutic effect. Therefore, in this paper, to deeply analyze the epidemic transmission with latency and quarantine states, we construct a class of health state-latent state -infected state-quarantined state-recovered state (SEIQR), epidemic model, with a power-law distribution of nodes based on considering the non-linear incidence formed by the psychological suppressor. Furthermore, the system's basic reproduction number R 0 and the equilibrium points' stability are discussed. The results show that R 0 depends on birth rate, death rate, recovery rate, vaccination rate, isolation rate, disease transmission rate, and network topology. Interestingly, the latency does not influence R . 0 And if < R 1, 0 system's disease-free equilibrium is global asymptotically stable, so is endemic equilibrium if > R 1.

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Dynamics of a time-delayed SIR epidemic model with logistic growth and saturated treatment

Cited by 38 publications

References 13 publications

Time-lagged response of malaria transmission to climate and land use change in a Colombian Amazonian Municipality: Implications for Early Warning Systems and Control Strategies

Time-lagged response of malaria transmission to climate and land use change in a Colombian Amazonian Municipality: Implications for Early Warning Systems and Control Strategies

Stability behavior of a two-susceptibility SHIR epidemic model with time delay in complex networks

Stability and optimal control strategy analysis for a class of SEIQR model with time delay on scale-free networks

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