# American Institute of Mathematical Sciences

December  2016, 21(10): 3315-3330. doi: 10.3934/dcdsb.2016099

## Minimizing $\mathcal R_0$ for in-host virus model with periodic combination antiviral therapy

 1 Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, United States 2 Department of Mathematics, University of Florida, 1400 Stadium Road, Gainesville, FL 32611

Received  December 2015 Revised  May 2016 Published  November 2016

The aim of this article is to provide formulas and properties of the basic reproduction number, $\mathcal R_0$, for a within-host virus model with periodic combination drug treatment. In particular, we extend and further results about how the phase difference between drug treatment can critically affect the asymptotic dynamics of model and corresponding $\mathcal R_0$. Our main theorem establishes that $\mathcal R_0$ is minimized for out-of-phase efficacies and maximized for in-phase efficacies in a special case where drug efficacies are bang-bang'' functions.
Citation: Cameron J. Browne, Sergei S. Pilyugin. Minimizing $\mathcal R_0$ for in-host virus model with periodic combination antiviral therapy. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3315-3330. doi: 10.3934/dcdsb.2016099
##### References:

show all references

##### References:
 [1] Zhikun She, Xin Jiang. Threshold dynamics of a general delayed within-host viral infection model with humoral immunity and two modes of virus transmission. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3835-3861. doi: 10.3934/dcdsb.2020259 [2] Qi Deng, Zhipeng Qiu, Ting Guo, Libin Rong. Modeling within-host viral dynamics: The role of CTL immune responses in the evolution of drug resistance. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3543-3562. doi: 10.3934/dcdsb.2020245 [3] Baba Issa Camara, Houda Mokrani, Evans K. Afenya. Mathematical modeling of glioma therapy using oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 565-578. doi: 10.3934/mbe.2013.10.565 [4] Sarra Delladji, Mohammed Belloufi, Badreddine Sellami. Behavior of the combination of PRP and HZ methods for unconstrained optimization. Numerical Algebra, Control & Optimization, 2021, 11 (3) : 377-389. doi: 10.3934/naco.2020032 [5] Weiyi Zhang, Zuhan Liu, Ling Zhou. Dynamics of a nonlocal diffusive logistic model with free boundaries in time periodic environment. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3767-3784. doi: 10.3934/dcdsb.2020256 [6] Rong Rong, Yi Peng. KdV-type equation limit for ion dynamics system. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021037 [7] Abdulrazzaq T. Abed, Azzam S. Y. Aladool. Applying particle swarm optimization based on Padé approximant to solve ordinary differential equation. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021008 [8] Naeem M. H. Alkoumi, Pedro J. Torres. Estimates on the number of limit cycles of a generalized Abel equation. Discrete & Continuous Dynamical Systems, 2011, 31 (1) : 25-34. doi: 10.3934/dcds.2011.31.25 [9] Wenjuan Zhao, Shunfu Jin, Wuyi Yue. A stochastic model and social optimization of a blockchain system based on a general limited batch service queue. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1845-1861. doi: 10.3934/jimo.2020049 [10] Jan Prüss, Laurent Pujo-Menjouet, G.F. Webb, Rico Zacher. Analysis of a model for the dynamics of prions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 225-235. doi: 10.3934/dcdsb.2006.6.225 [11] Jaume Llibre, Luci Any Roberto. On the periodic solutions of a class of Duffing differential equations. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 277-282. doi: 10.3934/dcds.2013.33.277 [12] Eduardo Casas, Christian Clason, Arnd Rösch. Preface special issue on system modeling and optimization. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021008 [13] Juntao Sun, Tsung-fang Wu. The number of nodal solutions for the Schrödinger–Poisson system under the effect of the weight function. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3651-3682. doi: 10.3934/dcds.2021011 [14] A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909 [15] Pankaj Kumar Tiwari, Rajesh Kumar Singh, Subhas Khajanchi, Yun Kang, Arvind Kumar Misra. A mathematical model to restore water quality in urban lakes using Phoslock. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3143-3175. doi: 10.3934/dcdsb.2020223 [16] Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399 [17] Nizami A. Gasilov. Solving a system of linear differential equations with interval coefficients. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2739-2747. doi: 10.3934/dcdsb.2020203 [18] Tian Hou, Yi Wang, Xizhuang Xie. Instability and bifurcation of a cooperative system with periodic coefficients. Electronic Research Archive, , () : -. doi: 10.3934/era.2021026 [19] Feng-Bin Wang, Xueying Wang. A general multipatch cholera model in periodic environments. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021105 [20] Juan Manuel Pastor, Javier García-Algarra, Javier Galeano, José María Iriondo, José J. Ramasco. A simple and bounded model of population dynamics for mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 53-70. doi: 10.3934/nhm.2015.10.53

2019 Impact Factor: 1.27