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Orozco-Gonzales JL, Dos Santos Benedito A, Cardona-Salgado D, Ferreira CP, de Oliveira Florentino H, Sepulveda-Salcedo LS, Vasilieva O. Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes. Math Biosci 2024; 372:109190. [PMID: 38631561 DOI: 10.1016/j.mbs.2024.109190] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2023] [Revised: 03/18/2024] [Accepted: 04/04/2024] [Indexed: 04/19/2024]
Abstract
This paper proposes a bidimensional modeling framework for Wolbachia invasion, assuming imperfect maternal transmission, incomplete cytoplasmic incompatibility, and direct infection loss due to thermal stress. Our model adapts to various Wolbachia strains and retains all properties of higher-dimensional models. The conditions for the durable coexistence of Wolbachia-carrying and wild mosquitoes are expressed using the model's parameters in a compact closed form. When the Wolbachia bacterium is locally established, the size of the remanent wild population can be assessed by a direct formula derived from the model. The model was tested for four Wolbachia strains undergoing laboratory and field trials to control mosquito-borne diseases: wMel, wMelPop, wAlbB, and wAu. As all these bacterial strains affect the individual fitness of mosquito hosts differently and exhibit different levels of resistance to temperature variations, the model helped to conclude that: (1) the wMel strain spreads faster in wild mosquito populations; (2) the wMelPop exhibits lower resilience but also guarantees the smallest size of the remanent wild population; (3) the wAlbB strain performs better at higher ambient temperatures than others; (4) the wAu strain is not sustainable and cannot persist in the wild mosquito population despite its resistance to high temperatures.
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Chinnathambi R, Rihan FA. Analysis and control of Aedes Aegypti mosquitoes using sterile-insect techniques with Wolbachia. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:11154-11171. [PMID: 36124585 DOI: 10.3934/mbe.2022520] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Combining Sterile and Incompatible Insect techniques can significantly reduce mosquito populations and prevent the transmission of diseases between insects and humans. This paper describes impulsive differential equations for the control of a mosquito with Wolbachia. Several interesting conditions are created when sterile male mosquitoes are released impulsively, ensuring both open- and closed-loop control. To determine the wild mosquito population size in real-time, we propose an open-loop control system, which uses impulsive and constant releases of sterile male mosquitoes. A closed-loop control scheme is also being investigated, which specifies the release of sterile mosquitoes according to the size of the wild mosquito population. To eliminate or reduce a mosquito population below a certain threshold, the Sterile insect technique involves mass releases of sterile insects. Numerical simulations verify the theoretical results.
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Affiliation(s)
- Rajivganthi Chinnathambi
- Division of Mathematics, School of Advances Sciences, Vellore Institute of Technology, Chennai, Tamilnadu-600 127, India
| | - Fathalla A Rihan
- Department of Mathematical Sciences, College of Science, United Arab Emirats University, Al-Ain 15551, UAE
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Bruzzese DJ, Schuler H, Wolfe TM, Glover MM, Mastroni JV, Doellman MM, Tait C, Yee WL, Rull J, Aluja M, Hood GR, Goughnour RB, Stauffer C, Nosil P, Feder JL. Testing the potential contribution of Wolbachia to speciation when cytoplasmic incompatibility becomes associated with host-related reproductive isolation. Mol Ecol 2021; 31:2935-2950. [PMID: 34455644 PMCID: PMC9290789 DOI: 10.1111/mec.16157] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Revised: 08/18/2021] [Accepted: 08/25/2021] [Indexed: 01/04/2023]
Abstract
Endosymbiont‐induced cytoplasmic incompatibility (CI) may play an important role in arthropod speciation. However, whether CI consistently becomes associated or coupled with other host‐related forms of reproductive isolation (RI) to impede the transfer of endosymbionts between hybridizing populations and further the divergence process remains an open question. Here, we show that varying degrees of pre‐ and postmating RI exist among allopatric populations of two interbreeding cherry‐infesting tephritid fruit flies (Rhagoletis cingulata and R. indifferens) across North America. These flies display allochronic and sexual isolation among populations, as well as unidirectional reductions in egg hatch in hybrid crosses involving southwestern USA males. All populations are infected by a Wolbachia strain, wCin2, whereas a second strain, wCin3, only co‐infects flies from the southwest USA and Mexico. Strain wCin3 is associated with a unique mitochondrial DNA haplotype and unidirectional postmating RI, implicating the strain as the cause of CI. When coupled with nonendosymbiont RI barriers, we estimate the strength of CI associated with wCin3 would not prevent the strain from introgressing from infected southwestern to uninfected populations elsewhere in the USA if populations were to come into secondary contact and hybridize. In contrast, cytoplasmic–nuclear coupling may impede the transfer of wCin3 if Mexican and USA populations were to come into contact. We discuss our results in the context of the general paucity of examples demonstrating stable Wolbachia hybrid zones and whether the spread of Wolbachia among taxa can be constrained in natural hybrid zones long enough for the endosymbiont to participate in speciation.
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Affiliation(s)
- Daniel J Bruzzese
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, USA
| | - Hannes Schuler
- Faculty of Science and Technology, Free University of Bozen-Bolzano, Bozen-Bolzano, Italy.,Competence Centre for Plant Health, Free University of Bozen-Bolzano, Bozen-Bolzano, Italy
| | - Thomas M Wolfe
- Department of Forest and Soil Sciences, Boku, University of Natural Resources and Life Sciences, Vienna, Austria
| | - Mary M Glover
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, USA
| | - Joseph V Mastroni
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, USA
| | - Meredith M Doellman
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, USA
| | - Cheyenne Tait
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, USA
| | - Wee L Yee
- United States Department of Agriculture, Temperate Tree Fruit & Vegetable Research Unit, Agricultural Research Service, Wapato, WA, USA
| | - Juan Rull
- Instituto de Ecología A.C., Xalapa, México.,LIEMEN-División Control Biológico de Plagas, PROIMI Biotecnología-CONICET, Tucumán, Argentina
| | | | - Glen Ray Hood
- Department of Biological Sciences, Wayne State University, Detroit, MI, USA
| | | | - Christian Stauffer
- Department of Forest and Soil Sciences, Boku, University of Natural Resources and Life Sciences, Vienna, Austria
| | - Patrik Nosil
- CEFE, University Montpellier, CNRS, EPHE, IRD, University Paul Valéry Montpellier 3, Montpellier, France.,Department of Biology, Utah State University, UT, USA
| | - Jeffery L Feder
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN, USA
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Wan H, Cui JA, Yang GJ. Risk estimation and prediction of the transmission of coronavirus disease-2019 (COVID-19) in the mainland of China excluding Hubei province. Infect Dis Poverty 2020; 9:116. [PMID: 32831142 PMCID: PMC7443853 DOI: 10.1186/s40249-020-00683-6] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2020] [Accepted: 05/28/2020] [Indexed: 11/24/2022] Open
Abstract
Background In December 2019, an outbreak of coronavirus disease (later named as COVID-19) was identified in Wuhan, China and, later on, detected in other parts of China. Our aim is to evaluate the effectiveness of the evolution of interventions and self-protection measures, estimate the risk of partial lifting control measures and predict the epidemic trend of the virus in the mainland of China excluding Hubei province based on the published data and a novel mathematical model. Methods A novel COVID-19 transmission dynamic model incorporating the intervention measures implemented in China is proposed. COVID-19 daily data of the mainland of China excluding Hubei province, including the cumulative confirmed cases, the cumulative deaths, newly confirmed cases and the cumulative recovered cases between 20 January and 3 March 2020, were archived from the National Health Commission of China (NHCC). We parameterize the model by using the Markov Chain Monte Carlo (MCMC) method and estimate the control reproduction number (Rc), as well as the effective daily reproduction ratio- Re(t), of the disease transmission in the mainland of China excluding Hubei province. Results The estimation outcomes indicate that Rc is 3.36 (95% CI: 3.20–3.64) and Re(t) has dropped below 1 since 31 January 2020, which implies that the containment strategies implemented by the Chinese government in the mainland of China are indeed effective and magnificently suppressed COVID-19 transmission. Moreover, our results show that relieving personal protection too early may lead to a prolonged disease transmission period and more people would be infected, and may even cause a second wave of epidemic or outbreaks. By calculating the effective reproduction ratio, we prove that the contact rate should be kept at least less than 30% of the normal level by April, 2020. Conclusions To ensure the pandemic ending rapidly, it is necessary to maintain the current integrated restrict interventions and self-protection measures, including travel restriction, quarantine of entry, contact tracing followed by quarantine and isolation and reduction of contact, like wearing masks, keeping social distance, etc. People should be fully aware of the real-time epidemic situation and keep sufficient personal protection until April. If all the above conditions are met, the outbreak is expected to be ended by April in the mainland of China apart from Hubei province.
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Affiliation(s)
- Hui Wan
- Jiangsu Key Lab for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
| | - Jing-An Cui
- Department of Mathematics, School of Science, Beijing University of Civil Engineering and Architecture, Beijing, China
| | - Guo-Jing Yang
- Hainan Medical University, Haikou, 571199, China. .,Swiss Tropical and Public Health Institute, Socinstrasse 57, Basel, CH-4002, Switzerland. .,University of Basel, Basel, Switzerland.
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Wan H, Cui JA, Yang GJ. Risk estimation and prediction of the transmission of coronavirus disease-2019 (COVID-19) in the mainland of China excluding Hubei province. Infect Dis Poverty 2020. [PMID: 32831142 DOI: 10.1101/2020.03.01.20029629] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/13/2023] Open
Abstract
BACKGROUND In December 2019, an outbreak of coronavirus disease (later named as COVID-19) was identified in Wuhan, China and, later on, detected in other parts of China. Our aim is to evaluate the effectiveness of the evolution of interventions and self-protection measures, estimate the risk of partial lifting control measures and predict the epidemic trend of the virus in the mainland of China excluding Hubei province based on the published data and a novel mathematical model. METHODS A novel COVID-19 transmission dynamic model incorporating the intervention measures implemented in China is proposed. COVID-19 daily data of the mainland of China excluding Hubei province, including the cumulative confirmed cases, the cumulative deaths, newly confirmed cases and the cumulative recovered cases between 20 January and 3 March 2020, were archived from the National Health Commission of China (NHCC). We parameterize the model by using the Markov Chain Monte Carlo (MCMC) method and estimate the control reproduction number (Rc), as well as the effective daily reproduction ratio- Re(t), of the disease transmission in the mainland of China excluding Hubei province. RESULTS The estimation outcomes indicate that Rc is 3.36 (95% CI: 3.20-3.64) and Re(t) has dropped below 1 since 31 January 2020, which implies that the containment strategies implemented by the Chinese government in the mainland of China are indeed effective and magnificently suppressed COVID-19 transmission. Moreover, our results show that relieving personal protection too early may lead to a prolonged disease transmission period and more people would be infected, and may even cause a second wave of epidemic or outbreaks. By calculating the effective reproduction ratio, we prove that the contact rate should be kept at least less than 30% of the normal level by April, 2020. CONCLUSIONS To ensure the pandemic ending rapidly, it is necessary to maintain the current integrated restrict interventions and self-protection measures, including travel restriction, quarantine of entry, contact tracing followed by quarantine and isolation and reduction of contact, like wearing masks, keeping social distance, etc. People should be fully aware of the real-time epidemic situation and keep sufficient personal protection until April. If all the above conditions are met, the outbreak is expected to be ended by April in the mainland of China apart from Hubei province.
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Affiliation(s)
- Hui Wan
- Jiangsu Key Lab for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
| | - Jing-An Cui
- Department of Mathematics, School of Science, Beijing University of Civil Engineering and Architecture, Beijing, China
| | - Guo-Jing Yang
- Hainan Medical University, Haikou, 571199, China.
- Swiss Tropical and Public Health Institute, Socinstrasse 57, Basel, CH-4002, Switzerland.
- University of Basel, Basel, Switzerland.
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Wan H, Cui JA, Yang GJ. Risk estimation and prediction of the transmission of coronavirus disease-2019 (COVID-19) in the mainland of China excluding Hubei province. Infect Dis Poverty 2020. [PMID: 32831142 DOI: 10.1101/2020.03.01.20029629v3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/26/2023] Open
Abstract
BACKGROUND In December 2019, an outbreak of coronavirus disease (later named as COVID-19) was identified in Wuhan, China and, later on, detected in other parts of China. Our aim is to evaluate the effectiveness of the evolution of interventions and self-protection measures, estimate the risk of partial lifting control measures and predict the epidemic trend of the virus in the mainland of China excluding Hubei province based on the published data and a novel mathematical model. METHODS A novel COVID-19 transmission dynamic model incorporating the intervention measures implemented in China is proposed. COVID-19 daily data of the mainland of China excluding Hubei province, including the cumulative confirmed cases, the cumulative deaths, newly confirmed cases and the cumulative recovered cases between 20 January and 3 March 2020, were archived from the National Health Commission of China (NHCC). We parameterize the model by using the Markov Chain Monte Carlo (MCMC) method and estimate the control reproduction number (Rc), as well as the effective daily reproduction ratio- Re(t), of the disease transmission in the mainland of China excluding Hubei province. RESULTS The estimation outcomes indicate that Rc is 3.36 (95% CI: 3.20-3.64) and Re(t) has dropped below 1 since 31 January 2020, which implies that the containment strategies implemented by the Chinese government in the mainland of China are indeed effective and magnificently suppressed COVID-19 transmission. Moreover, our results show that relieving personal protection too early may lead to a prolonged disease transmission period and more people would be infected, and may even cause a second wave of epidemic or outbreaks. By calculating the effective reproduction ratio, we prove that the contact rate should be kept at least less than 30% of the normal level by April, 2020. CONCLUSIONS To ensure the pandemic ending rapidly, it is necessary to maintain the current integrated restrict interventions and self-protection measures, including travel restriction, quarantine of entry, contact tracing followed by quarantine and isolation and reduction of contact, like wearing masks, keeping social distance, etc. People should be fully aware of the real-time epidemic situation and keep sufficient personal protection until April. If all the above conditions are met, the outbreak is expected to be ended by April in the mainland of China apart from Hubei province.
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Affiliation(s)
- Hui Wan
- Jiangsu Key Lab for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
| | - Jing-An Cui
- Department of Mathematics, School of Science, Beijing University of Civil Engineering and Architecture, Beijing, China
| | - Guo-Jing Yang
- Hainan Medical University, Haikou, 571199, China.
- Swiss Tropical and Public Health Institute, Socinstrasse 57, Basel, CH-4002, Switzerland.
- University of Basel, Basel, Switzerland.
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Taghikhani R, Sharomi O, Gumel AB. Dynamics of a two-sex model for the population ecology of dengue mosquitoes in the presence of Wolbachia. Math Biosci 2020; 328:108426. [PMID: 32712316 DOI: 10.1016/j.mbs.2020.108426] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2020] [Revised: 07/15/2020] [Accepted: 07/15/2020] [Indexed: 11/30/2022]
Abstract
The release of Wolbachia-infected mosquitoes into the population of wild mosquitoes is one of the promising biological control method for combating the population abundance of mosquitoes that cause deadly diseases, such as dengue. In this study, a new two-sex mathematical model for the population ecology of dengue mosquitoes and disease is designed and used to assess the population-level impact of the periodic release of Wolbachia-infected mosquitoes. Rigorous analysis of the model, which incorporates many of the lifecycle features of dengue disease and the cytoplasmic incompatibility property of Wolbachia bacterium in mosquitoes, reveal that the disease-free equilibrium of the model is locally-asymptotically stable whenever a certain epidemiological threshold, known as the reproduction number of the model (denoted by R0W), is less than unity. The model is shown, using centre manifold theory, to undergo the phenomenon of backward bifurcation at R0W=1. The consequence of this bifurcation is that Wolbachia may not persist, or dengue disease may not be effectively-controlled, when R0W is less than unity. Such persistence and elimination will depend on the initial sizes of the sub-populations of the model. Two mechanisms were identified for which the backward bifurcation phenomenon can be removed. When backward bifurcation does not occur, the associated non-trivial disease-free equilibrium is shown to be globally-asymptotically stable when the reproduction number of the model is less than unity. Numerical simulations, using data relevant to dengue transmission dynamics in northern Queensland, Australia, shows that releasing Wolbachia-infected mosquitoes every three weeks, for a one-year duration, can lead to the effective control of the population abundance of the local wild mosquitoes, and that such effective control increases with increasing number of Wolbachia-infected mosquitoes released (resulting in the reduction of over 90% of the wild mosquito population from their baseline values). Furthermore, simulations show that releasing only adult male Wolbachia-infected mosquitoes provide more beneficial population-level impact (in terms of reducing the population abundance of the wild mosquitoes), in comparison to releasing adult female Wolbachia-infected mosquitoes. Increasing the frequency of Wolbachia release (e.g., from the default release frequency of every three weeks to weekly) does not significantly affect the effectiveness of the Wolbachia-based control program in curtailing the local abundance of the wild mosquitoes. Finally, it was shown that the cytoplasmic incompatibility property of Wolbachia bacterium does not significantly affect the effectiveness of the Wolbachia-based mosquito control strategy implemented in the community.
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Affiliation(s)
- Rahim Taghikhani
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA
| | | | - Abba B Gumel
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA; Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa.
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