Primary: 34K20, 92D30.

Export file:

Format

• RIS(for EndNote,Reference Manager,ProCite)
• BibTex
• Text

Content

• Citation Only
• Citation and Abstract

Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes

## Abstract    Related pages

A delayed vector-bias model for malaria transmission with incubation period in mosquitoes is studied. The delay $\tau$ corresponds to the time necessary for a latently infected vector to become an infectious vector. We prove that the global stability is completely determined by the threshold parameter, $R_0(\tau)$. If $R_0(\tau)\leq1$, the disease-free equilibrium is globally asymptotically stable. If $R_0(\tau)>1$ a unique endemic equilibrium exists and is globally asymptotically stable. We apply our results to Ross-MacDonald malaria models with an incubation period (extrinsic or intrinsic).
Figure/Table
Supplementary
Article Metrics

Citation: Cruz Vargas-De-León. Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes. Mathematical Biosciences and Engineering, 2012, 9(1): 165-174. doi: 10.3934/mbe.2012.9.165

• 1. Cruz Vargas-De-León, Noé Chan Chí, Eric Ávila Vales, Global analysis of virus dynamics model with logistic mitosis, cure rate and delay in virus production, Mathematical Methods in the Applied Sciences, 2015, 38, 4, 646, 10.1002/mma.3096
• 2. Bruno Buonomo, Analysis of a malaria model with mosquito host choice and bed-net control, International Journal of Biomathematics, 2015, 08, 06, 1550077, 10.1142/S1793524515500771
• 3. Bruno Buonomo, Cruz Vargas-De-León, Effects of Mosquitoes Host Choice on Optimal Intervention Strategies for Malaria Control, Acta Applicandae Mathematicae, 2014, 132, 1, 127, 10.1007/s10440-014-9894-z
• 4. Lourdes Esteva, Cristobal Vargas, Cruz Vargas de León, The role of asymptomatics and dogs on leishmaniasis propagation, Mathematical Biosciences, 2017, 293, 46, 10.1016/j.mbs.2017.08.006
• 5. Xiaomei Feng, Shigui Ruan, Zhidong Teng, Kai Wang, Stability and backward bifurcation in a malaria transmission model with applications to the control of malaria in China, Mathematical Biosciences, 2015, 266, 52, 10.1016/j.mbs.2015.05.005
• 6. Bruno Buonomo, Cruz Vargas-De-León, Stability and bifurcation analysis of a vector-bias model of malaria transmission, Mathematical Biosciences, 2013, 242, 1, 59, 10.1016/j.mbs.2012.12.001
• 7. Zhiting Xu, Yiyi Zhang, Traveling wave phenomena of a diffusive and vector-bias malaria model, Communications on Pure and Applied Analysis, 2015, 14, 3, 923, 10.3934/cpaa.2015.14.923
• 8. Xia Wang, Yuming Chen, Shengqiang Liu, Global dynamics of a vector-borne disease model with infection ages and general incidence rates, Computational and Applied Mathematics, 2017, 10.1007/s40314-017-0560-8