Climate-denying rumor propagation in a coupled socio-climate model: Impact on average global temperature

and the edges are connections between the individuals or between individuals and the groups they belong to. Each individual is assumed to be in one of the following states: sk denotes the proportion of susceptible individuals who are susceptible to the rumor about climate change but are not exposed to the rumor, hk, hesitator is the individual who is exposed to the rumor but hesitates to believe or reject the rumor. If they accept it, they propagate the rumor. Other- wise, they reject it. iB is the proportion of believers who believe climate change is not real and share the rumor individually and in groups, and iR is the proportion of rejectors who reject the rumor, believing that climate change is real, and do not forward the rumor. The equations for the rumor propagation involve ordinary differential equations and are as follows [49]: s0 kðtÞ ¼ B b�ckskðtÞ P jðpðjjkÞÞ pj iBj ðtÞ þ a�ck P jðpðjjkÞÞ pj iBj ðtÞ þ g�ckiRk ðtÞ �G �m�dBskðtÞ iBk ðtÞ þ �G �m�dsiRk ðtÞ þ �G �m�driBk ðtÞ mskðtÞ h0 kðtÞ ¼ b�cskðtÞk P jðpðjjkÞÞ pj iBj ðtÞ ðZðTÞ þ εÞ�ck P jðpðjjkÞÞ pj hjðtÞ þ �G �m�dBskðtÞiBk ðtÞ �G �m�doðTÞhkðtÞ �G �m�dzhkðtÞ mhkðtÞ i0 Bk ðtÞ ¼ ZðTÞ�ck P jðpðjjkÞÞ pj hjðtÞ a�ck P jðpðjjkÞÞ pj iBj ðtÞ þ �G �m�doðTÞhkðtÞ �G �m�dr iBk ðtÞ miBk ðtÞ i0 Rk ðtÞ ¼ ε�ck P jðpðjjkÞÞ pj hjðtÞ g�ckiRk ðtÞ þ �G �m�dzhkðtÞ �G �m�dsiRk ðtÞ miRk ðtÞ ð1:1Þ Social media features, like entering and leaving the network at any stage, are considered in this model. Individuals joining the network always fall into the susceptible category, and the

number of individuals joining the network per unit of time is B. An individual can exit the net- work at any time, and hence the exiting rate at which an individual exits the network μ is included in each compartment. Since both individual and group propagation are considered, both parameters are considered separately. β is the hesitating probability with which a suscep- tible individual becomes a hesitator individual, whereas the hesitating probability in groups is B. The probability that a hesitator individual believes the rumor is η, and in groups, this proba- bility is ω. Similarly, a hesitator individual rejects the rumor with probability �; in groups, this probability is z. A forgetting mechanism is also included in this model, along with believing and rejecting mechanisms. Individuals will forget the rumor and their opinion about it, as time passes and revert to the initial susceptible state. The probability with which the believer and rejector individuals forget the rumor is α and γ, respectively. The term p(j|k) denotes the probability with which an edge with degree k connects to a node with degree j. The respective rates in groups are considered as ρ and σ. Apart from the probabilities, the average rate of indi- vidual contact is �c, and the average rate at which messages are transmitted per group is �d. The average network degree is k with X groups having m members on average, with the average degree for the group for an individual being �G. PLOS ONE Climate-denying rumor propagation in a coupled socio-climate model: Impact on average global temperature

PLOS ONE | https://doi.org/10.1371/journal.pone.0317338 January 16, 2025 4 / 18