I was wondering if you could help me out with a differential equation / mathematical modeling problem. I am struggling with finding the basic reproductive number also known as R0 for these three models. I have tried to use the Jacobian method by finding the largest eigenvalue, but i am not sure if it is correct. I have tried to use the next generation method but i don’t understand how to find the F and V^-1 value for the matrices. Below is the paper with three models, each with assumptions, stability analysis done. All that needs to be done is the R0 value, for each and an analysis of how the R0 value can contribute to the equilibrium.
ASSUMPTIONS FOR THE BASIC MODEL The basic model the researchers decided to study revolved around the classicalpop-culture zombie which has the qualities of moving slow, being cannibalistic and undead. Inthis model there are three basic categories that are considered. The ﬁrst group is the“susceptible” category. These humans can die due to natural causes (6) or by zombieencounter(ﬁ) and they have a constant birth rate (1’1). If a human from the susceptible groupdefeats a zombie during their encounter, then they will turning into a zombie themselves (a). The second category is the “removed” group. This group is made of up the dead, andhumans are placed in there if they lost a zombie encounter or died a natural cause. Themagnitude of this group will decrease when the members resurrect (g). The third category they considered is the zombie category. The amount of zombies willincrease when someone from the removed group resurrects and when a susceptible loses anbattle with zombie. For simpliﬁcation reasons, the researchers will allow only humans (no animals) tobecome infected with the zombie disease. As for the zombies, they are only allowed to cravehuman flesh. Zombies themselves can be placed in the removed category if their head is removed from theirbody or their brain is destroyed. Zombies can only attack humans, not other zombies. When evaluating what happens during the short timescale, we can ignore any birth or death ratesgoing on in the model.
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