1
|
Wheeler J, Rosengart A, Jiang Z, Tan K, Treutle N, Ionides EL. Informing policy via dynamic models: Cholera in Haiti. PLoS Comput Biol 2024; 20:e1012032. [PMID: 38683863 PMCID: PMC11081515 DOI: 10.1371/journal.pcbi.1012032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2023] [Revised: 05/09/2024] [Accepted: 03/29/2024] [Indexed: 05/02/2024] Open
Abstract
Public health decisions must be made about when and how to implement interventions to control an infectious disease epidemic. These decisions should be informed by data on the epidemic as well as current understanding about the transmission dynamics. Such decisions can be posed as statistical questions about scientifically motivated dynamic models. Thus, we encounter the methodological task of building credible, data-informed decisions based on stochastic, partially observed, nonlinear dynamic models. This necessitates addressing the tradeoff between biological fidelity and model simplicity, and the reality of misspecification for models at all levels of complexity. We assess current methodological approaches to these issues via a case study of the 2010-2019 cholera epidemic in Haiti. We consider three dynamic models developed by expert teams to advise on vaccination policies. We evaluate previous methods used for fitting these models, and we demonstrate modified data analysis strategies leading to improved statistical fit. Specifically, we present approaches for diagnosing model misspecification and the consequent development of improved models. Additionally, we demonstrate the utility of recent advances in likelihood maximization for high-dimensional nonlinear dynamic models, enabling likelihood-based inference for spatiotemporal incidence data using this class of models. Our workflow is reproducible and extendable, facilitating future investigations of this disease system.
Collapse
Affiliation(s)
- Jesse Wheeler
- Statistics Department, University of Michigan, Ann Arbor, Michigan, United States of America
| | - AnnaElaine Rosengart
- Statistics and Data Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
| | - Zhuoxun Jiang
- Statistics Department, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Kevin Tan
- Wharton Statistics and Data Science, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
| | - Noah Treutle
- Statistics Department, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Edward L. Ionides
- Statistics Department, University of Michigan, Ann Arbor, Michigan, United States of America
| |
Collapse
|
2
|
Wang S, Nie L. Global analysis of a diffusive Cholera model with multiple transmission pathways, general incidence and incomplete immunity in a heterogeneous environment. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:4927-4955. [PMID: 38872521 DOI: 10.3934/mbe.2024218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2024]
Abstract
With the consideration of the complexity of the transmission of Cholera, a partially degenerated reaction-diffusion model with multiple transmission pathways, incorporating the spatial heterogeneity, general incidence, incomplete immunity, and Holling type Ⅱ treatment was proposed. First, the existence, boundedness, uniqueness, and global attractiveness of solutions for this model were investigated. Second, one obtained the threshold condition $ \mathcal{R}_{0} $ and gave its expression, which described global asymptotic stability of disease-free steady state when $ \mathcal{R}_{0} < 1 $, as well as the maximum treatment rate as zero. Further, we obtained the disease was uniformly persistent when $ \mathcal{R}_{0} > 1 $. Moreover, one used the mortality due to disease as a branching parameter for the steady state, and the results showed that the model undergoes a forward bifurcation at $ \mathcal{R}_{0} $ and completely excludes the presence of endemic steady state when $ \mathcal{R}_{0} < 1 $. Finally, the theoretical results were explained through examples of numerical simulations.
Collapse
Affiliation(s)
- Shengfu Wang
- College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
| | - Linfei Nie
- College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
| |
Collapse
|
3
|
Wang N, Zhang L, Teng Z. Dynamics in a reaction-diffusion epidemic model via environmental driven infection in heterogenous space. JOURNAL OF BIOLOGICAL DYNAMICS 2022; 16:373-396. [PMID: 33724911 DOI: 10.1080/17513758.2021.1900428] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2020] [Accepted: 02/27/2021] [Indexed: 06/12/2023]
Abstract
In this paper, a reaction-diffusion SIR epidemic model via environmental driven infection in heterogeneous space is proposed. To reflect the prevention and control measures of disease in allusion to the susceptible in the model, the nonlinear incidence function Ef(S) is applied to describe the protective measures of susceptible. In the general spatially heterogeneous case of the model, the well-posedness of solutions is obtained. The basic reproduction number R0 is calculated. When R0≤1 the global asymptotical stability of the disease-free equilibrium is obtained, while when R0>1 the model is uniformly persistent. Furthermore, in the spatially homogeneous case of the model, when R0>1 the global asymptotic stability of the endemic equilibrium is obtained. Lastly, the numerical examples are enrolled to verify the open problems.
Collapse
Affiliation(s)
- Ning Wang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, People's Republic of China
| | - Long Zhang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, People's Republic of China
| | - Zhidong Teng
- College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, People's Republic of China
| |
Collapse
|
4
|
A reaction-advection-diffusion model of cholera epidemics with seasonality and human behavior change. J Math Biol 2022; 84:34. [PMID: 35381862 DOI: 10.1007/s00285-022-01733-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2021] [Revised: 11/19/2021] [Accepted: 03/02/2022] [Indexed: 11/27/2022]
Abstract
Cholera is a water- and food-borne infectious disease caused by V. cholerae. To investigate multiple effects of human behavior change, seasonality and spatial heterogeneity on cholera spread, we propose a reaction-advection-diffusion model that incorporates human hosts and aquatic reservoir of V. cholerae. We derive the basic reproduction number [Formula: see text] for this system and then establish a threshold type result on its global dynamics in terms of [Formula: see text]. Further, we show that the bacterial loss at the downstream end of the river due to water flux can reduce the disease risk, and describe the asymptotic behavior of [Formula: see text] for small and large diffusion in a special case (where the diffusion rates of infected human and the pathogen are constant). We also study the transmission dynamics at the early stage of cholera outbreak numerically, and find that human behavior change may lower the infection level and delay the disease peak. Moreover, the relative rate of bacterial loss, together with convection rate, plays an important role in identifying the severely infected areas. Meanwhile spatial heterogeneity may dilute or amplify cholera infection, which in turn would increase the complexity of disease spread.
Collapse
|
5
|
Stability Analysis and Optimal Control of a Fractional Cholera Epidemic Model. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6030157] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
In this paper, a fractional model for the transmission dynamics of cholera was developed. In invariant regions of the model, solutions were generated. Disease-free and endemic equilibrium points were obtained. The basic reproduction number was evaluated, and the sensitivity analysis was performed. Under the support of Pontryagin’s maximum principle, the fractional order optimal control was obtained. Furthermore, an optimal strategy was discussed, which minimized the total number of infected individuals and the costs associated with control. Treatment, vaccination, and awareness programs were regarded as three means to reduce the number of infected. Finally, numerical simulations and cost-effectiveness analysis were presented to show the result that the best strategy was the combination of treatment and awareness programs.
Collapse
|
6
|
Lata K, Misra AK, Takeuchi Y. Modeling the Effectiveness of TV and Social Media Advertisements on the Dynamics of Water-Borne Diseases. INT J BIOMATH 2021. [DOI: 10.1142/s1793524521500698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Cholera is a serious threat to the health of human-kind all over the world and its control is a problem of great concern. In this context, a nonlinear mathematical model to control the prevalence of cholera disease is proposed and analyzed by incorporating TV and social media advertisements as a dynamic variable. It is considered that TV and social media ads propagate the knowledge among the people regarding the severe effects of cholera disease on human health along with its precautionary measures. It is also assumed that the mode of transmission of cholera disease among susceptible individuals is due to consumption of contaminated drinking water containing Vibrio cholerae. Moreover, the propagation of knowledge through TV and social media ads makes the people aware to adopt precautionary measures and also the aware people make some effectual efforts to washout the bacteria from the aquatic environment. Model analysis reveals that increase in the washout rate of bacteria due to aware individuals causes the stability switch. It is found that TV and social media ads have the potential to reduce the number of infectives in the region and thus control the cholera epidemic. Numerical simulation is performed for a particular set of parameter values to support the analytical findings.
Collapse
Affiliation(s)
- Kusum Lata
- Department of Mathematical & Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki 225 003, India
| | - A. K. Misra
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221 005, India
| | - Y. Takeuchi
- College of Science and Engineering, Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan
| |
Collapse
|
7
|
|
8
|
Fitzgibbon WE, Morgan JJ, Webb GF, Wu Y. Modelling the aqueous transport of an infectious pathogen in regional communities: application to the cholera outbreak in Haiti. J R Soc Interface 2020; 17:20200429. [PMID: 32752993 DOI: 10.1098/rsif.2020.0429] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
A mathematical model is developed to describe the dynamics of the spread of a waterborne disease among communities located along a flowing waterway. The model is formulated as a system of reaction-diffusion-advection partial differential equations in this spatial setting. The compartments of the model consist of susceptible, infected, and recovered individuals in the communities along the waterway, together with a term representing the pathogen load in each community and a term representing the spatial concentration of pathogens flowing along the waterway. The model is applied to the cholera outbreak in Haiti in 2010.
Collapse
Affiliation(s)
| | - Jeffrey J Morgan
- Department of Mathematics, University of Houston, Houston, TX 77204, USA
| | - Glenn F Webb
- Department of Mathematics, Vanderbilt University, Nashville, TN 37212, USA
| | - Yixiang Wu
- Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA
| |
Collapse
|
9
|
Lemos-Paião AP, Silva CJ, Torres DFM, Venturino E. Optimal Control of Aquatic Diseases: A Case Study of Yemen’s Cholera Outbreak. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2020. [DOI: 10.1007/s10957-020-01668-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
|
10
|
An epidemic model for cholera with optimal control treatment. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2017. [DOI: 10.1016/j.cam.2016.11.002] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
|
11
|
Du Z, Peng R. A priori L∞ estimates for solutions of a class of reaction-diffusion systems. J Math Biol 2015; 72:1429-39. [PMID: 26141826 DOI: 10.1007/s00285-015-0914-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2015] [Revised: 05/10/2015] [Indexed: 11/28/2022]
Abstract
In this short paper, we establish a priori L∞-norm estimates for solutions of a class of reaction-diffusion systems which can be used to model the spread of infectious disease. The developed technique may find applications in other reaction-diffusion systems.
Collapse
Affiliation(s)
- Zengji Du
- Department of Mathematics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, China
| | - Rui Peng
- Department of Mathematics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, China.
| |
Collapse
|