Ross-Macdonald models: Which one should we use?

Simoy, Mario Ignacio; Aparicio, Juan Pablo

doi:10.1016/j.actatropica.2020.105452

Cited by 10 publications

(7 citation statements)

References 42 publications

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“…In the existing literature, Simon et al 17 investigated the differences between exponential and nonexponential distributions in homogeneous models. Their findings indicated that variations in disease stage distributions have an impact on the transmission process.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…In the existing literature, Simon et al 17 . investigated the differences between exponential and nonexponential distributions in homogeneous models.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Feng et al 16 explored the impact of different distributions of disease stages on intervention effectiveness. Simoy et al 17 considered arbitrary distributions of infectious stages in a vector-borne disease model and discussed the significance of actual distributions of infectious stages.…”

mentioning

confidence: 99%

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Global dynamics of heterogeneous epidemic models with exponential and nonexponential latent period distributions

Zang,

Lin,

Liu

2024

Stud Appl Math

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Many epidemic models assume an exponential distribution for the latent stage, but this may not accurately represent reality and could impact disease transmission predictions. Previous studies for short time scale models have shown that the choice of latency distribution affects estimates of the epidemic peak, time to peak, and infection eradication time, but has little effect on the final infection size. However, it is unclear if these conclusions hold for long time scale models. To address this, we investigate the impact of different latency distributions on disease dynamics in long‐term models, comparing them with short‐term models. We propose two susceptible‐exposed‐infected‐hospitalized‐recovered () models with multiple groups, using exponential and gamma distributions for latency. We derive the basic reproduction number () for both models and prove the global stability of the equilibrium points. We conduct numerical simulations and find that the gamma distribution may lead to larger epidemic peak sizes and longer peak times compared to the exponential distribution. However, the impact of latency distribution on estimating the peak and time to peak is smaller in long‐term models than in short‐term models. Additionally, the effect on the final total infected size is negligible regardless of the time scale. Therefore, when analyzing long‐term epidemic dynamics using heterogeneity models, the choice of latency distribution does not significantly affect the results. Assuming an exponential distribution for the latency is sufficient for simplifying the model and facilitating analysis. Our study provides valuable insights for selecting appropriate mathematical models in epidemiology.

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Section: Conclusion and Discussionmentioning

confidence: 99%

“…In the existing literature, Simon et al 17 . investigated the differences between exponential and nonexponential distributions in homogeneous models.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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Global dynamics of heterogeneous epidemic models with exponential and nonexponential latent period distributions

Zang,

Lin,

Liu

2024

Stud Appl Math

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“…Over the years, a variety of mathematical models have been developed to aid in understanding the malaria transmission mechanism, improving control strategies, and reducing the global impact of malaria. The very first malaria model was developed by Ronald Ross [3,4].…”

Section: Introductionmentioning

confidence: 99%

Bayesian spatiotemporal modelling and mapping of malaria risk among children aged below 5 years in Ghana

Takramah,

Afrane,

Aheto

2024

Preprint

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Background Malaria is a significant public health problem, particularly among children aged 6-59 months who bear the greatest burden of this disease. Malaria transmission is high and more pronounced in poor tropical and subtropical areas of the world. Climate change is positively correlated with the geographical distribution of malaria vectors. There is substantial evidence of spatial and temporal differences in under-five malaria risk. Thus, the study aimed to create intelligent maps of smooth relative risk of malaria in children under-5 years that highlights high and low malaria burden in space and time to support malaria prevention, control, and elimination efforts. Method The study extracted and merged the required data on malaria among children aged 6-59 months from 2014 Ghana Demographic and Health Surveys (GDHS), 2016 and 2019 Ghana Malaria Indicator Surveys (GMIS). The outcome variable of interest is the count of children aged 6-59 months with positive test on rapid diagnostic test (RDT) kit. Bayesian Hierarchical Spatiotemporal models were specified to estimate and map spatiotemporal variations in the relative risk of malaria. The existence of local clustering was assessed using local indicator of spatial association (LISA) and the points were mapped to display significant local clusters, hotpot, and cold spot communities. Results The number of positive malaria cases in children aged 6-59 months decreased marginally between the 2014 and 2019 DHS survey periods. Smooth relative risk of malaria among children aged 6-59 months has consistently increased in the Northern and Eastern regions between 2014 and 2019. Socioeconomic and climatic factors such as household size [Posterior Mean: -0.198 (95% CrI: 3.52, 80.95)], rural area [Posterior Mean: 1.739 (95% CrI: 0.581, 2.867)], rainfall [Posterior Mean: 0.003 (95% CrI: 0.001, 0.005)], and maximum temperature [Posterior Mean: -1.069 (95% CrI: -2.135, -0.009)] have all been shown as statistically significant predictors of malaria risk in children aged 6-59 months. Hot spot DHS clusters with a significantly high relative risk of malaria among children aged 6-59 months were repeatedly detected in the Ashanti region between 2014 and 2019. Conclusion The findings would provide policymakers with practical and insightful information for the equitable distribution of scarce health resources targeted at reducing the burden of malaria and its associated mortality among children under-five years.

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“…Compartmental mathematical models for vector-borne diseases are vastly found in the literature [ 31 , 32 , 33 ], and are mainly based on and inspired by the Ross–McDonald malaria model [ 34 ]. In particular, there is a significant number of articles associated with mathematical modeling of malaria dynamics [ 35 , 36 , 37 , 38 , 39 , 40 ].…”

Section: Introductionmentioning

confidence: 99%

Collateral Effects of Insecticide-Treated Nets on Human and Environmental Safety in an Epidemiological Model for Malaria with Human Risk Perception

Gutiérrez-Jara

Vogt-Geisse

Cabrera

2022

IJERPH

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Malaria remains a major health problem in many parts of the world, including Sub-Saharan Africa. Insecticide-treated nets, in combination with other control measures, have been effective in reducing malaria incidence over the past two decades. Nevertheless, there are concerns about improper handling and misuse of nets, producing possible health effects from intoxication and collateral environmental damage. The latter is caused, for instance, from artisanal fishing. We formulate a model of impulsive differential equations to describe the interplay between malaria dynamics, human intoxication, and ecosystem damage; affected by human awareness to these risks and levels of net usage. Our results show that an increase in mosquito net coverage reduces malaria prevalence and increases human intoxications. In addition, a high net coverage significantly reduces the risk perception to disease, naturally increases the awareness for intoxications from net handling, and scarcely increases the risk perception to collateral damage from net fishing. According to our model, campaigns aiming at reducing disease prevalence or intoxications are much more successful than those creating awareness to ecosystem damage. Furthermore, we can observe from our results that introducing closed fishing periods reduces environmental damage more significantly than strategies directed towards increasing the risk perception for net fishing.

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Ross-Macdonald models: Which one should we use?

Cited by 10 publications

References 42 publications

Global dynamics of heterogeneous epidemic models with exponential and nonexponential latent period distributions

Global dynamics of heterogeneous epidemic models with exponential and nonexponential latent period distributions

Bayesian spatiotemporal modelling and mapping of malaria risk among children aged below 5 years in Ghana

Collateral Effects of Insecticide-Treated Nets on Human and Environmental Safety in an Epidemiological Model for Malaria with Human Risk Perception

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