Malaria Models with Spatial Effects

Gao, Daozhou; Ruan, Shigui

doi:10.1002/9781118630013.ch6

Cited by 6 publications

(7 citation statements)

References 48 publications

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“…Recently, Gao et al [21] showed that the finding of Dye and Hasibeder [12] and Hasibeder and Dye [25] remains true for a malaria model with human and/or mosquito migration. For more studies on this topic, the readers may refer to two review articles by Cosner [8] and Gao and Ruan [20].…”

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confidence: 99%

Effects of travel frequency on the persistence of mosquito-borne diseases

Chen¹,

Gao²

2020

Discrete &Amp; Continuous Dynamical Systems - B

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Travel frequency of people varies widely with occupation, age, gender, ethnicity, income, climate and other factors. Meanwhile, the distribution of the numbers of times people in different regions or with different travel behaviors bitten by mosquitoes may be nonuniform. To reflect these two heterogeneities, we develop a multipatch model to study the impact of travel frequency and human biting rate on the spatial spread of mosquito-borne diseases. The human population in each patch is divided into four classes: susceptible unfrequent, infectious unfrequent, susceptible frequent, and infectious frequent. The basic reproduction number R 0 is defined. It is shown that the diseasefree equilibrium is globally asymptotically stable if R 0 ≤ 1, and there is a unique endemic equilibrium that is globally asymptotically stable if R 0 > 1. A more detailed study is conducted on the single patch model. We use analytical and numerical methods to demonstrate that the model without considering the difference of humans in travel frequency mostly underestimates the risk of infection. Numerical simulations suggest that the greater the difference in travel frequency, the larger the underestimate of the transmission potential. In addition, the basic reproduction number R 0 may decreasingly, or increasingly, or nonmonotonically vary when more people travel frequently.

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Effects of travel frequency on the persistence of mosquito-borne diseases

Chen¹,

Gao²

2020

Discrete &Amp; Continuous Dynamical Systems - B

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“…Various factors, such as biological invasion, global warming, environmental degradation, increased international travel, and economic development, continue to provide more opportunities for the emerging and re-emerging of many infectious diseases, the spatial spread of diseases has become a subject of continuing interest to both theoreticians and empiricists (Gao and Ruan [23], Hethcote [30], Martens [46], Murray [47], Rass and Radcliffe [49], Ruan [50]). To better understand the geographic spread of infectious diseases, the spatial effects have been extensively included into mathematical models and have been quantitatively studied.…”

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Traveling wave solutions in a two-group epidemic model with latent period

Zhao

Ruan

2017

Nonlinearity

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“…In the recent years, the impact of population dispersal has received increasing attention, and many mathematical patch models are formulated to investigate this hot issue (see [24,3,14] and the references cited therein). Here, the patches can be cities, towns, states, countries or other appropriate community divisions.…”

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An SIR epidemic model with vaccination in a patchy environment

Cui¹,

Qiu²,

Ding³

2017

MBE

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In this paper, an SIR patch model with vaccination is formulated to investigate the effect of vaccination coverage and the impact of human mobility on the spread of diseases among patches. The control reproduction number Rv is derived. It shows that the disease-free equilibrium is unique and is globally asymptotically stable if Rv< 1, and unstable if Rv>1. The sufficient condition for the local stability of boundary equilibria and the existence of equilibria are obtained for the case n=2. Numerical simulations indicate that vaccines can control and prevent the outbreak of infectious in all patches while migration may magnify the outbreak size in one patch and shrink the outbreak size in other patch.

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Malaria Models with Spatial Effects

Cited by 6 publications

References 48 publications

Effects of travel frequency on the persistence of mosquito-borne diseases

Effects of travel frequency on the persistence of mosquito-borne diseases

Traveling wave solutions in a two-group epidemic model with latent period

An SIR epidemic model with vaccination in a patchy environment

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