(Solved): Patch i Patch j Figure 5: Flow diagram showing disease progression within each patch (S->E->I- ...
Patch
iPatch
jFigure 5: Flow diagram showing disease progression within each patch
(S->E->I->R)and migration between patches
iand
j(dashed double arrows). The terms
m_(ij)^(x)and
m_(ji)^(x)represent migration rates of compartment
xin{S,E,I,R}between patches. Transmission occurs locally in each patch at rates
\beta _(i)S_(i)(I_(i))/(N_(i))and
\beta _(j)S_(j)(I_(j))/(N_(j)). 0.5 Model Equations for Disease Spread Between Patches
iand
jWe consider a human population divided into two spatial patches,
iand
j, connected by migration. In each patch, individuals are classified into four epidemiological compartments: susceptible
(S), exposed
(E), infectious
(I), and recovered
(R). The total population in patch
kin{i,j}is
N_(k)=S_(k)+E_(k)+I_(k)+R_(k)Transmission occurs locally within each patch due to contact between susceptible and infectious individuals. Migration occurs bidirectionally between patches for each compartment. 10 Model Equations The full system of ordinary differential equations describing the dynamics is:
(dS_(i))/(dt)=\Lambda _(i)-(\beta _(i)S_(i)I_(i))/(N_(i))-\mu _(i)S_(i)+m_(ji)^(S)S_(j)-m_(ij)^(S)S_(i),
(dE_(i))/(dt)=(\beta _(i)S_(i)I_(i))/(N_(i))-(\sigma +\mu _(i))E_(i)+m_(ji)^(E)E_(j)-m_(ij)^(E)E_(i),
(dI_(i))/(dt)=\sigma E_(i)-(\gamma +\mu _(i)+\delta _(i))I_(i)+m_(ji)^(I)I_(j)-m_(ij)^(I)I_(i),
(dR_(i))/(dt)=\gamma I_(i)-\mu _(i)R_(i)+m_(ji)^(R)R_(j)-m_(ij)^(R)R_(i),
(dS_(j))/(dt)=\Lambda _(j)-(\beta _(j)S_(j)I_(j))/(N_(j))-\mu _(j)S_(j)+m_(ij)^(S)S_(i)-m_(ji)^(S)S_(j),
(dE_(j))/(dt)=(\beta _(j)S_(j)I_(j))/(N_(j))-(\sigma +\mu _(j))E_(j)+m_(ij)^(E)E_(i)-m_(ji)^(E)E_(j),
(dI_(j))/(dt)=\sigma E_(j)-(\gamma +\mu _(j)+\delta _(j))I_(j)+m_(ij)^(I)I_(i)-m_(ji)^(I)I_(j),
(dR_(j))/(dt)=\gamma I_(j)-\mu _(j)R_(j)+m_(ij)^(R)R_(i)-m_(ji)^(R)R_(j).Parameter Definitions \table[[Parameter,Description],[
\Lambda _(k),Recruitment rate into the susceptible class in patch
kHi guys this is my model graph and the equations please correct or add where is missing . My research is Mathematical modeling of Mpox and its effects on migration and human population dispersal
