Pandemics and immune memory in the noisy Penna model

In the noisy Penna model of ageing, instead of counting the number of defective loci which eventually kill an individual, the noise describing the health status of individuals is introduced. This white noise is composed of two components: the environmental one and the personal one. If the sum of both trespasses the limit set for the individuals homeodynamics the individual dies. The energy of personal fluctuations depends on the number of defective loci expressed in the individuals genome. Environmental fluctuations, the same for all individuals can include some signals, corresponding to the exposition to pathogens which could be dangerous for a fraction of the organisms. Personal noise and the component of random environmental fluctuations, when superimposed on the signal can be life threatening if they are stronger than the limit set for individuals homeodynamics. Nevertheless, some organisms survive the period of dangerous signal and they may remember the signal in the future, like antigens are remembered by our immune systems. Unfortunately, this memory weakens with time and, even worse, some additional defective genes are switched on during the ageing. If the same pathogens (signals) emerge during the lifespan of the population, a fraction of the population could remember it and could respond by increasing the resistance to it. Again, unfortunately for some individuals, their memory could be too weak and their own health status has worsened due to the accumulated mutations, they have to die. Though, a fraction of individuals can survive the pandemics due to the immune memory, but a fraction of population has no such a memory because they were born after the last pandemic or they didnt notice this pandemic. Our simple model, by implementing the noise instead of deterministic threshold of genetic defects, describes how the impact of pandemics on populations depends on the time which elapsed between the two incidents and how the different age groups of populations can respond for the second pandemic.

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