Projected spread models

Abstract

We present a disease transmission model that considers both explicit and non-explicit factors. This approach is crucial for accurate prediction and control of infectious disease spread. In this paper, we extend the spread model from our previous works (Ban et al. in Chaos Solitons Fractals 150:111106, 2021; Ban et al. in Chaos 33(6):063144, 2023; Ban et al. in J Math Biol 86(3):40, 2023; Ban et al. in Chaos 32(10):103113, 2023) to a projected spread model that considers both hidden and explicit types. Additionally, we provide the spread rate for the projected spread model corresponding to the topological and random models. Furthermore, examples and numerical results are provided to illustrate the theory.

Keywords: Projected spread model; Random spread model; Spread rate; Topological spread model.

Fig. 1

The graph of 0-block code defined by and in

Fig. 2

The graph of 0-block code defined by and in

Fig. 3

The potential 1-patterns

Fig. 4

A potential 2-pattern

Fig. 5

Not a potential 2-pattern

Fig. 6

Fig. 7

The first four levels of a possible realization of

Fig. 8

An illustration of how to induce from via

Fig. 9

An illustration of how to induce from

Fig. 10

Examples of a topological model with three types. The solid line represents experimental values, while the dashed line represents theoretical values. In this case, the spread rate is numerically approximated by averaging over 300 simulations

Fig. 11

Examples of a random model for 0-block code. The solid line represents experimental values, while the dashed line represents theoretical values. In this case, the spread rate is numerically approximated by averaging over 300 simulations

Fig. 12

Examples of a random model for 1-block code. The solid line represents experimental values, while the dashed line represents theoretical values. In this case, the spread rate is numerically approximated by averaging over 300 simulations

Fig. 13

Potential 2-patterns initiated with

Fig. 14

Potential 2-patterns initiated with

Fig. 15

A 2-pattern in induced from a 4-pattern in

Fig. 16

Examples of a random model for 2-block code. The solid line represents experimental values, while the dashed line represents theoretical values. In this case, the spread rate is numerically approximated by averaging over 300 simulations