Markovian Approach for Exploring Competitive Diseases with Heterogeneity-Evidence from COVID-19 and Influenza in China.

Due to the complex interactions between multiple infectious diseases, the spreading of diseases in human bodies can vary when people are exposed to multiple sources of infection at the same time. Typically, there is heterogeneity in individuals' responses to diseases, and the transmission routes of different diseases also vary. Therefore, this paper proposes an SIS disease spreading model with individual heterogeneity and transmission route heterogeneity under the simultaneous action of two competitive infectious diseases. We derive the theoretical epidemic spreading threshold using quenched mean-field theory and perform numerical analysis under the Markovian method. Numerical results confirm the reliability of the theoretical threshold and show the inhibitory effect of the proportion of fully competitive individuals on epidemic spreading. The results also show that the diversity of disease transmission routes promotes disease spreading, and this effect gradually weakens when the epidemic spreading rate is high enough. Finally, we find a negative correlation between the theoretical spreading threshold and the average degree of the network. We demonstrate the practical application of the model by comparing simulation outputs to temporal trends of two competitive infectious diseases, COVID-19 and seasonal influenza in China.

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks.

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0 with and without mortality, respectively, and prove that RM1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.

Individualized epidemic spreading models predict epilepsy surgery outcomes: A pseudo-prospective study.

Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients, but up to 50% of patients continue to have seizures one year after the resection. In order to aid presurgical planning and predict postsurgical outcome on a patient-by-patient basis, we developed a framework of individualized computational models that combines epidemic spreading with patient-specific connectivity and epileptogeneity maps: the Epidemic Spreading Seizure and Epilepsy Surgery framework (ESSES). ESSES parameters were fitted in a retrospective study (N = 15) to reproduce invasive electroencephalography (iEEG)-recorded seizures. ESSES reproduced the iEEG-recorded seizures, and significantly better so for patients with good (seizure-free, SF) than bad (nonseizure-free, NSF) outcome. We illustrate here the clinical applicability of ESSES with a pseudo-prospective study (N = 34) with a blind setting (to the resection strategy and surgical outcome) that emulated presurgical conditions. By setting the model parameters in the retrospective study, ESSES could be applied also to patients without iEEG data. ESSES could predict the chances of good outcome after any resection by finding patient-specific model-based optimal resection strategies, which we found to be smaller for SF than NSF patients, suggesting an intrinsic difference in the network organization or presurgical evaluation results of NSF patients. The actual surgical plan overlapped more with the model-based optimal resection, and had a larger effect in decreasing modeled seizure propagation, for SF patients than for NSF patients. Overall, ESSES could correctly predict 75% of NSF and 80.8% of SF cases pseudo-prospectively. Our results show that individualised computational models may inform surgical planning by suggesting alternative resections and providing information on the likelihood of a good outcome after a proposed resection. This is the first time that such a model is validated with a fully independent cohort and without the need for iEEG recordings.

Individualized computational models of epilepsy surgery capture some of the key aspects of seizure propagation and the resective surgery. It is to be established whether this information can be integrated during the presurgical evaluation of the patient to improve surgical planning and the chances of a good surgical outcome. Here we address this question with a pseudo-prospective study that applies a computational framework of seizure propagation and epilepsy surgery­the ESSES framework­in a pseudo-prospective study mimicking the presurgical conditions. We found that within this pseudo-prospective setting, ESSES could correctly predict 75% of NSF and 80.8% of SF cases. This finding suggests the potential of individualised computational models to inform surgical planning by suggesting alternative resections and providing information on the likelihood of a good outcome after a proposed resection.