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Mathematical Modelling of Dengue Transmission with Intervention Strategies Using Fractional Derivatives. Bull Math Biol 2022; 84:138. [DOI: 10.1007/s11538-022-01096-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2022] [Accepted: 10/10/2022] [Indexed: 11/02/2022]
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2
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Rashkov P, Kooi BW. Complexity of host-vector dynamics in a two-strain dengue model. JOURNAL OF BIOLOGICAL DYNAMICS 2021; 15:35-72. [PMID: 33357025 DOI: 10.1080/17513758.2020.1864038] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 12/06/2020] [Indexed: 06/12/2023]
Abstract
We introduce a compartmental host-vector model for dengue with two viral strains, temporary cross-immunity for the hosts, and possible secondary infections. We study the conditions on existence of endemic equilibria where one strain displaces the other or the two virus strains co-exist. Since the host and vector epidemiology follow different time scales, the model is described as a slow-fast system. We use the geometric singular perturbation technique to reduce the model dimension. We compare the behaviour of the full model with that of the model with a quasi-steady approximation for the vector dynamics. We also perform numerical bifurcation analysis with parameter values from the literature and compare the bifurcation structure to that of previous two-strain host-only models.
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Affiliation(s)
- Peter Rashkov
- Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
| | - Bob W Kooi
- Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
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3
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Guo M, Hu L, Nie LF. Stochastic dynamics of the transmission of Dengue fever virus between mosquitoes and humans. INT J BIOMATH 2021. [DOI: 10.1142/s1793524521500625] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Considering the impact of environmental white noise on the quantity and behavior of vector of disease, a stochastic differential model describing the transmission of Dengue fever between mosquitoes and humans, in this paper, is proposed. By using Lyapunov methods and Itô’s formula, we first prove the existence and uniqueness of a global positive solution for this model. Further, some sufficient conditions for the extinction and persistence in the mean of this stochastic model are obtained by using the techniques of a series of stochastic inequalities. In addition, we also discuss the existence of a unique stationary distribution which leads to the stochastic persistence of this disease. Finally, several numerical simulations are carried to illustrate the main results of this contribution.
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Affiliation(s)
- Manjing Guo
- College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, P. R. China
| | - Lin Hu
- College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, P. R. China
| | - Lin-Fei Nie
- College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, P. R. China
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Luo Y, Zhang L, Teng Z, Zheng T. Stability and bifurcation for a stochastic differential algebraic Holling-II predator–prey model with nonlinear harvesting and delay. INT J BIOMATH 2021. [DOI: 10.1142/s1793524521500194] [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
In this paper, a stochastic delayed differential algebraic predator–prey model with Michaelis–Menten-type prey harvesting is proposed. Due to the influence of gestation delay and stochastic fluctuations, the proposed model displays a complex dynamics. Criteria on the local stability of the interior equilibrium are established, and the effect of gestation delay on the model dynamics is discussed. Taking the gestation delay and economic profit as bifurcation parameters, Hopf bifurcation and singularity induced bifurcation can occur as they cross through some critical values, respectively. Moreover, the solution of the model will blow up in a limited time when delay [Formula: see text]. Then, we calculate the fluctuation intensity of the stochastic fluctuations by Fourier transform method, which is the key to illustrate the effect of stochastic fluctuations. Finally, we demonstrate our theoretical results by numerical simulations.
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Affiliation(s)
- Yantao Luo
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. China
| | - Long Zhang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. China
| | - Zhidong Teng
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. China
| | - Tingting Zheng
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. China
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Ndii MZ, Mage AR, Messakh JJ, Djahi BS. Optimal vaccination strategy for dengue transmission in Kupang city, Indonesia. Heliyon 2020; 6:e05345. [PMID: 33204872 PMCID: PMC7648192 DOI: 10.1016/j.heliyon.2020.e05345] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2019] [Revised: 06/24/2020] [Accepted: 10/22/2020] [Indexed: 11/22/2022] Open
Abstract
Dengue is a public health problem with around 390 million cases annually and is caused by four distinct serotypes. Infection by one of the serotypes provides lifelong immunity to that serotype but have a higher chance of attracting the more dangerous forms of dengue in subsequent infections. Therefore, a perfect strategy against dengue is required. Dengue vaccine with 42-80% efficacy level has been licensed for the use in reducing disease transmission. However, this may increase the likelihood of obtaining the dangerous forms of dengue. In this paper, we have developed single and two-serotype dengue mathematical models to investigate the effects of vaccination on dengue transmission dynamics. The model is validated against dengue data from Kupang city, Indonesia. We investigate the effects of vaccination on seronegative and seropositive individuals and perform a global sensitivity analysis to determine the most influential parameters of the model. A sensitivity analysis suggests that the vaccination rate, the transmission probability and the biting rate have greater effects on the reduction of the proportion of dengue cases. Interestingly, with vaccine implementation, the mosquito-related parameters do not have significant impact on the reduction in the proportion of dengue cases. If the vaccination is implemented on seronegative individuals only, it may increase the likelihood of obtaining the severe dengue. To reduce the proportion of severe dengue cases, it is better to vaccinate seropositive individuals. In the context of Kupang City where the majority of individuals have been infected by at least one dengue serotype, the implementation of vaccination strategy is possible. However, understanding the serotype-specific differences is required to optimise the delivery of the intervention.
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Affiliation(s)
- Meksianis Z Ndii
- Department of Mathematics, The University of Nusa Cendana, Kupang-NTT, Indonesia
| | - Ananda R Mage
- Department of Mathematics, The University of Nusa Cendana, Kupang-NTT, Indonesia
| | - Jakobis J Messakh
- Department of Building Engineering Education, The University of Nusa Cendana, Kupang-NTT, Indonesia
| | - Bertha S Djahi
- Department of Computer Science, The University of Nusa Cendana, Kupang-NTT, Indonesia
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Irving AT, Rozario P, Kong PS, Luko K, Gorman JJ, Hastie ML, Chia WN, Mani S, Lee BPH, Smith GJD, Mendenhall IH, Larman HB, Elledge SJ, Wang LF. Robust dengue virus infection in bat cells and limited innate immune responses coupled with positive serology from bats in IndoMalaya and Australasia. Cell Mol Life Sci 2020; 77:1607-1622. [PMID: 31352533 PMCID: PMC11104837 DOI: 10.1007/s00018-019-03242-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2019] [Revised: 07/10/2019] [Accepted: 07/22/2019] [Indexed: 01/19/2023]
Abstract
Natural reservoir hosts can sustain infection of pathogens without succumbing to overt disease. Multiple bat species host a plethora of viruses, pathogenic to other mammals, without clinical symptoms. Here, we detail infection of bat primary cells, immune cells, and cell lines with Dengue virus. While antibodies and viral RNA were previously detected in wild bats, their ability to sustain infection is not conclusive. Old-world fruitbat cells can be infected, producing high titres of virus with limited cellular responses. In addition, there is minimal interferon (IFN) response in cells infected with MOIs leading to dengue production. The ability to support in vitro replication/production raises the possibility of bats as a transient host in the life cycle of dengue or similar flaviviruses. New antibody serology evidence from Asia/Pacific highlights the previous exposure and raises awareness that bats may be involved in flavivirus dynamics and infection of other hosts.
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Affiliation(s)
| | | | | | | | - Jeffrey J Gorman
- QIMR Berghofer Medical Research Institute, Herston, QLD, Australia
| | - Marcus L Hastie
- QIMR Berghofer Medical Research Institute, Herston, QLD, Australia
| | - Wan Ni Chia
- Duke-NUS Medical School, Singapore, Singapore
| | | | | | | | | | | | - Stephen J Elledge
- Harvard University Medical School, Boston, MA, 02115, USA
- Howard Hughes Medical Institute, Brigham and Women's Hospital, Boston, MA, 02115, USA
| | - Lin-Fa Wang
- Duke-NUS Medical School, Singapore, Singapore.
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Sasmal SK, Takeuchi Y, Nakaoka S. T-Cell mediated adaptive immunity and antibody-dependent enhancement in secondary dengue infection. J Theor Biol 2019; 470:50-63. [DOI: 10.1016/j.jtbi.2019.03.010] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2018] [Revised: 02/13/2019] [Accepted: 03/12/2019] [Indexed: 11/26/2022]
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