An expanded model describing viral evolution within organism was proposed as an extension of the SEIRS model with illness symptoms - SEI[Is]RS. It has been implemented in a self-organizing, multi-agent system based on social networks and social time model. This article presents the results of simulation of simultaneous spreading within the population of two viral strains which provide total cross immunity to each other. The effect of displacing one viral strain by another, supported by empirical observations, is also present in obtained simulation results. It might have important consequences for genetic and antigenic diversity of viruses in populations. Epidemic, SEIRS, virus spreading, social network, I. INTRODUCTION The work regarding modeling of disease spread in populations had been carried out as early as in the 18 th century by Daniel Bernoulli [1], even before Louis Pasteur suggested that diseases might be caused by microorganisms. Together with the development of information technology and numerical methods of solving equations there appeared possibilities to build and analyse more and more complex epidemiological models, for example with a probabilistic mechanism of transition between disease stages [2]. This article presents the results of simulated presence of two viruses in the population which provide mutual 100% cross immunity. Such scenarios occur in case of fast mutating viruses, such as the influenza virus. The research on the second immunological response [3] indicates that this may also be the case for a wider range of viral subtypes, significantly different genetically, especially in a short period after recovery. Special attention was paid on attempting to explain empirically observed displacement of one viral strain by another. The possibility resulting from this phenomenon to use an appropriately modified virus as a vaccine was also analysed. The studies were conducted with a multiagent system, designed for this simulation, and SEI[Is]RS as the model of viral evolution in the body, described in the subsequent parts of this article. Manuscript received March 16, 2008. Radosław Nielek, Polish Japanese Institute of Information Technology, ul Koszykowa 86, 02-008 Warszawa (radek@zetema.pl) Aleksander Wawer, Institute of Computer Science POLISH ACADEMY OF SCIENCES, ul. Ordona 21 01-237 Warszawa, Poland (axf@zetema.pl). Romuald Kotowski, Polish Japanese Institute of Information Technology, ul Koszykowa 86, 02-008 Warszawa (rkotow@pjwstk.edu.pl) II. SEI[IS]RS – A NEW MODEL OF VIRUS EVOLUTION SIRS (Susceptible – Infected – Resistant - Susceptible) and SEIRS (Susceptible – Evolution – Infected – Resistant - Susceptible), are the two most popular models of virus evolution in the organism, used to simulate incidence of non-mortal diseases. The modification proposed in this article is based on the addition of another stage, namely, “illness symptoms”. Individuals limit their social activities during this stage. One can express this as a decrease in the number of their daily contacts with other individuals. It is explained by at least two interacting effects: a lower amount of energy due to disease symptoms and social responsibility – “I am limiting myself from contacting others because I don’t want to infect them”. The effects related to changes in the behaviour of individuals due to a disease or only information about a disease are considered by some authors to be incurring the highest economic costs for the society [4], sometimes even higher than the outbreak of pandemic itself. The length of virus evolution stages are variable and depend on many factors in reality. According to the research done in this field, disease stages can change many times as a result of taken medications, genetic conditions, diet or a wide range of external and internal factors. The model of bi-directional, probabilistic transitions between disease stages was presented for AIDS in [2]. Fig. 1 presents the sequence of virus evolution stages in the organism which was used by the authors of the article to simulate epidemic. The values marked on the OX axis with Greek letters are set as simulation parameters. All individuals in stages “evolution”, “infectious” or “illness symptoms” are infected. Transitions between stages are possible only in one direction. The model does not take into account differences between individuals regarding their resistance to illnesses or their recovery rates. Fig. 1. Virus evolution in an individual with the time. As the model takes into account non-mortal diseases caused by fast mutating viruses, the resistance acquired by an individual after experiencing a disease is only temporary. It is related to the immunological memory of individuals, which weakens with time since the last virus infection, for most but Two Antigenically Indistinguishable Viruses in a Population Radoslaw Nielek, Aleksander Wawer, Romuald Kotowski Susceptible (S) Evolution (E) Infectious (I) Resistant (R) Susceptible (S) Illness symptoms (Is) Infected time 0 α χ δ β Proceedings of the World Congress on Engineering 2008 Vol III WCE 2008, July 2 - 4, 2008, London, U.K. ISBN:978-988-17012-4-4 WCE 2008