2025/02/12 by Sascha Franck, Franck, Sascha, Cornelia Pokalyuk +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #60J80 #60K35 #92D25 #92D30 #COVID-19 epidemiological studies #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2502.08475
openalex publication_date 2025/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a generalized version of the frog model to describe the invasion of a parasite population in a spatially structured immobile host population with host immunity on the integer line. Parasites move according to simple symmetric random walks and try to infect any host they meet. Hosts, however, own an immunity against the parasites that protects them from infection for a random number of attacks. Once a host gets infected, it and the infecting parasite die, and a random number of offspring parasites is generated. We show that the positivity of the survival probability of parasites only depends on the mean offspring and mean height of immunity. Furthermore, we prove through the construction of a renewal structure that given survival of the parasite population parasites invade the host population at linear speed under relatively mild assumptions on the host immunity distribution.