We consider temporal networks that are a union of disjoint cliques at all times $t$. We call temporal networks that consist of disjoint cliques temporal clique graphs. We extend the exact solution of mean-field SIS epidemics with self-infections on the complete graph, derived by Prasse et al. [Chaos 31, 063115 (2021)], to all temporal clique graphs. Temporal clique graphs cover a range of commonplace models of network dynamics, including metapopulation models and specifically random-walker-induced temporal graphs. Since the exact solution of mean-field SIS on temporal clique graphs is piecewise (i.e., given by different functions on different intervals), we apply further approximations and find an approximate expression for the expected fraction of infected individuals, called the prevalence $y\left(t\right)$, at all times $t$, with as parameters only the infection rate $\beta$, the curing rate $\delta$, and the average size ${\theta }_j$ of each clique $j$ in the steady state of the network dynamics. Our strongest assumption is that the contact network is static and in its steady state, effectively ignoring all graph dynamics. Despite the drastic assumptions, in ignoring any temporal aspects of the contact network, the approximation is remarkably accurate, when the number of walkers is high. We assess our prevalence approximation (15) and indicate and explain its accuracy.

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• Epidemic
• Epidemic prevalence
• Spreading
• Evolving networks
• Epidemic spreading
• SIS model