Threshold dynamics of a malaria transmission model in periodic environment

<p style='text-indent:20px;'>Huanglongbing (HLB) is a disease of citrus that caused by phloem-restricted bacteria of the Candidatus Liberibacter group. In this paper, we present a HLB transmission model to investigate the effects of temperature-dependent latent periods and seasonality on the spread of HLB. We first establish disease free dynamics in terms of a threshold value <inline-formula><tex-math id="M1">\begin{document}$ R^p_0 $\end{document}</tex-math></inline-formula>, and then introduce the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> and show the threshold dynamics of HLB with respect to <inline-formula><tex-math id="M3">\begin{document}$ R^p $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>. Numerical simulations are further provided to illustrate our analytic results.</p>

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Backward bifurcation in a malaria transmission model

Journal of Biological Dynamics ◽

10.1080/17513758.2020.1771443 ◽

2020 ◽

Vol 14 (1) ◽

pp. 368-388 ◽

Cited By ~ 1

Author(s):

Yanyuan Xing ◽

Zhiming Guo ◽

Jian Liu

Keyword(s):

Malaria Transmission ◽

Backward Bifurcation ◽

Transmission Model

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A Malaria Transmission Model Predicts Holoendemic, Hyperendemic, and Hypoendemic Transmission Patterns Under Varied Seasonal Vector Dynamics

Journal of Medical Entomology ◽

10.1093/jme/tjz186 ◽

2019 ◽

Vol 57 (2) ◽

pp. 568-584

Author(s):

Vardayani Ratti ◽

Dorothy I Wallace

Keyword(s):

Steady State ◽

Anopheles Gambiae ◽

Malaria Transmission ◽

Entomological Inoculation Rate ◽

Disease Prevalence ◽

Larval Habitat ◽

Transmission Model ◽

Habitat Availability ◽

Human Populations ◽

The Relationship

Abstract A model is developed of malaria (Plasmodium falciparum) transmission in vector (Anopheles gambiae) and human populations that include the capacity for both clinical and parasite suppressing immunity. This model is coupled with a population model for Anopheles gambiae that varies seasonal with temperature and larval habitat availability. At steady state, the model clearly distinguishes uns hypoendemic transmission patterns from stable hyperendemic and holoendemic patterns of transmission. The model further distinguishes hyperendemic from holoendemic disease based on seasonality of infection. For hyperendemic and holoendemic transmission, the model produces the relationship between entomological inoculation rate and disease prevalence observed in the field. It further produces expected rates of immunity and prevalence across all three endemic patterns. The model does not produce mesoendemic transmission patterns at steady state for any parameter choices, leading to the conclusion that mesoendemic patterns occur during transient states or as a result of factors not included in this study. The model shows that coupling the effect of varying larval habitat availability with the effects of clinical and parasite-suppressing immunity is enough to produce known patterns of malaria transmission.

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Stability, Bifurcation and Optimal Control Analysis of a Malaria Model in a Periodic Environment

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2017-0221 ◽

2018 ◽

Vol 19 (6) ◽

pp. 627-642 ◽

Cited By ~ 2

Author(s):

Prabir Panja ◽

Shyamal Kumar Mondal ◽

Joydev Chattopadhyay

Keyword(s):

Optimal Control ◽

Disease Transmission ◽

Existence Condition ◽

Infected Mosquito ◽

Transmission Model ◽

Control Analysis ◽

Periodic Environment ◽

Vector Population ◽

Autonomous Case ◽

Disease Transmission Model

AbstractIn this paper, a malaria disease transmission model has been developed. Here, the disease transmission rates from mosquito to human as well as human to mosquito and death rate of infected mosquito have been constituted by two variabilities: one is periodicity with respect to time and another is based on some control parameters. Also, total vector population is divided into two subpopulations such as susceptible mosquito and infected mosquito as well as the total human population is divided into three subpopulations such as susceptible human, infected human and recovered human. The biologically feasible equilibria and their stability properties have been discussed. Again, the existence condition of the disease has been illustrated theoretically and numerically. Hopf-bifurcation analysis has been done numerically for autonomous case of our proposed model with respect to some important parameters. At last, a optimal control problem is formulated and solved using Pontryagin’s principle. In numerical simulations, different possible combination of controls have been illustrated including the comparisons of their effectiveness.

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