Aleph::CA::SIR_Rule< Engine > Class Template Reference

SIR epidemic transition rule. More...

#include <tpl_ca_stochastic_rules.H>

Public Types
using	engine_type = Engine

Public Member Functions
	SIR_Rule (double beta, double gamma, std::uint64_t master_seed=0)
	Build an SIR rule with infection rate beta and recovery rate gamma.
double	beta () const noexcept
double	gamma () const noexcept
std::uint64_t	master_seed () const noexcept
void	set_master_seed (std::uint64_t s) noexcept
	Replace the master seed.
template<typename State , std::size_t Rank>
State	operator() (const State &current, Neighbor_View< State > neighbours, const Cell_Context< Rank > &ctx) const
	Compute the next SIR state for cell current.

Private Attributes
double	beta_
double	gamma_
std::uint64_t	master_seed_

Detailed Description

template<typename Engine = std::mt19937_64>
class Aleph::CA::SIR_Rule< Engine >

SIR epidemic transition rule.

Synchronous discrete-time SIR on the cellular automaton:

• R stays R.
• I recovers to R with probability gamma, else stays I.
• S becomes I with probability 1 - (1 - beta)^k where k is the number of infected neighbours; else stays S.

When R0 = beta * <degree> / gamma < 1, the epidemic asymptotically goes extinct on the lattice for any finite seed of infections; the unit tests cover this regime explicitly.

Template Parameters

Engine

RNG engine; defaults to std::mt19937_64.

Definition at line 241 of file tpl_ca_stochastic_rules.H.

Member Typedef Documentation

engine_type

template<typename Engine = std::mt19937_64>

using Aleph::CA::SIR_Rule< Engine >::engine_type = Engine

Definition at line 248 of file tpl_ca_stochastic_rules.H.

Constructor & Destructor Documentation

SIR_Rule()

template<typename Engine = std::mt19937_64>

Aleph::CA::SIR_Rule< Engine >::SIR_Rule ( double  beta, double  gamma, std::uint64_t  master_seed = 0  )

inline

Build an SIR rule with infection rate beta and recovery rate gamma.

Parameters

[in]	beta	per-contact infection probability.
[in]	gamma	per-step recovery probability.
[in]	master_seed	master seed forwarded to cell_seed().

Exceptions

std::domain_error

if either probability is outside [0, 1].

Definition at line 259 of file tpl_ca_stochastic_rules.H.

References ah_domain_error_if, Aleph::CA::SIR_Rule< Engine >::beta(), Aleph::blossom_maximum_cardinality_matching(), and Aleph::CA::SIR_Rule< Engine >::gamma().

Member Function Documentation

beta()

template<typename Engine = std::mt19937_64>

double Aleph::CA::SIR_Rule< Engine >::beta ( ) const

inlinenoexcept

Returns

the configured infection probability.

Definition at line 268 of file tpl_ca_stochastic_rules.H.

References Aleph::CA::SIR_Rule< Engine >::beta_.

Referenced by Aleph::CA::SIR_Rule< Engine >::SIR_Rule().

gamma()

template<typename Engine = std::mt19937_64>

double Aleph::CA::SIR_Rule< Engine >::gamma ( ) const

inlinenoexcept

Returns

the configured recovery probability.

Definition at line 274 of file tpl_ca_stochastic_rules.H.

References Aleph::CA::SIR_Rule< Engine >::gamma_.

Referenced by Aleph::CA::SIR_Rule< Engine >::SIR_Rule().

master_seed()

template<typename Engine = std::mt19937_64>

std::uint64_t Aleph::CA::SIR_Rule< Engine >::master_seed ( ) const

inlinenoexcept

Returns

the master seed.

Definition at line 280 of file tpl_ca_stochastic_rules.H.

References Aleph::CA::SIR_Rule< Engine >::master_seed_.

operator()()

template<typename Engine = std::mt19937_64>

template<typename State , std::size_t Rank>

State Aleph::CA::SIR_Rule< Engine >::operator() ( const State &  current, Neighbor_View< State >  neighbours, const Cell_Context< Rank > &  ctx  ) const

inline

Compute the next SIR state for cell current.

Template Parameters

State	integral or enum-typed cell state convertible to SIR_Cell.
Rank	lattice rank carried by ctx.

Parameters

[in]	current	current centre-cell state.
[in]	neighbours	read-only neighbour values.
[in]	ctx	per-cell context with step and coord.

Returns

next state produced by the rule.

Exceptions

Any	exception thrown by the RNG constructor.

Definition at line 303 of file tpl_ca_stochastic_rules.H.

References Aleph::CA::SIR_Rule< Engine >::beta_, Aleph::blossom_maximum_cardinality_matching(), Aleph::CA::SIR_Rule< Engine >::gamma_, Aleph::CA::I, Aleph::CA::SIR_Rule< Engine >::master_seed_, Aleph::CA::R, and Aleph::CA::uniform_unit().

set_master_seed()

template<typename Engine = std::mt19937_64>

void Aleph::CA::SIR_Rule< Engine >::set_master_seed ( std::uint64_t  s )

inlinenoexcept

Replace the master seed.

Definition at line 286 of file tpl_ca_stochastic_rules.H.

References Aleph::CA::SIR_Rule< Engine >::master_seed_.

Member Data Documentation

beta_

template<typename Engine = std::mt19937_64>

double Aleph::CA::SIR_Rule< Engine >::beta_

private

Definition at line 243 of file tpl_ca_stochastic_rules.H.

Referenced by Aleph::CA::SIR_Rule< Engine >::beta(), and Aleph::CA::SIR_Rule< Engine >::operator()().

gamma_

template<typename Engine = std::mt19937_64>

double Aleph::CA::SIR_Rule< Engine >::gamma_

private

Definition at line 244 of file tpl_ca_stochastic_rules.H.

Referenced by Aleph::CA::SIR_Rule< Engine >::gamma(), and Aleph::CA::SIR_Rule< Engine >::operator()().

master_seed_

template<typename Engine = std::mt19937_64>

std::uint64_t Aleph::CA::SIR_Rule< Engine >::master_seed_

private

Definition at line 245 of file tpl_ca_stochastic_rules.H.

Referenced by Aleph::CA::SIR_Rule< Engine >::master_seed(), Aleph::CA::SIR_Rule< Engine >::operator()(), and Aleph::CA::SIR_Rule< Engine >::set_master_seed().

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The documentation for this class was generated from the following file:

• tpl_ca_stochastic_rules.H