Local Immunodeficiency: Role of Neutral Viruses
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Local Immunodeficiency: Role of Neutral Viruses Leonid Bunimovich1 · Longmei Shu2 Received: 13 March 2020 / Accepted: 25 September 2020 © Society for Mathematical Biology 2020
Abstract This paper analyzes the role of neutral viruses in the phenomenon of local immunodeficiency. We show that, even in the absence of altruistic viruses, neutral viruses can support the existence of persistent viruses and thus local immunodeficiency. However, in all such cases neutral viruses can maintain only bounded (relatively small) concentration of persistent viruses. Moreover, in all such cases the state of local immunodeficiency could only be marginally stable, while it is known that altruistic viruses can maintain stable local immunodeficiency. We also present an absolutely minimal cross-immunoreactivity network where a stable and robust state of local immunodeficiency can be maintained. It is now a challenge to synthetic biology to build such small networks with stable local immunodeficiency. Another important challenge for biology is to understand which types of viruses can play a role of persistent, altruistic and neutral ones and whether a role which a given virus plays depends on the structure (topology) of a given cross-immunoreactivity network. Keywords Cross-immunoreactivity network · Local immunodeficiency · Neutral · Altruistic and persistent viruses
1 Introduction Local immunodeficiency (LI) is a recently discovered phenomenon (Skums et al. 2015) that appears in diseases characterized by cross-immunoreactivity of the corresponding pathogens (viruses). Examples of such diseases include hepatitis C, HIV, dengue, influenza, etc. (Hattori et al. 1998; Campo et al. 2014; Nowak and May
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Longmei Shu [email protected] Leonid Bunimovich [email protected]
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School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
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Mathematics and Science Center, Emory University, Suite W401, 400 Dowman Drive, Atlanta, GA 30322, USA 0123456789().: V,-vol
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1991, 2000; Yoshioka et al. 1997; Wodarz 2003; Nowak et al. 1990, 1991). The phenomenon of local immunodeficiency means that some persistent antigens (viruses) manage to escape immune response because they are protected by altruistic viruses that take virtually all the response of the host’s immune system on themselves. This discovery was made through the (numerical) analysis of a new model of hepatitis C dynamics (evolution) that explained clinical and experimental observations that previous evolution models (and theory) of hepatitis C failed to explain. Remarkably, this new mathematical model has fewer (types of) variables than the previous ones (Wodarz 2003). Yet this new model makes much more delicate exploration of the wellknown phenomenon of cross-immunoreactivity than all previous evolution models of infectious diseases, including the fundamental dynamics model of HIV (Nowak et al. 1990, 1991; Nowak and May 1991). Namely, the new model does not assume that all cross-immunoreactivity interactions betw
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